Straight Line Graphs www mathsrevision com S 4

Straight Line Graphs www. mathsrevision. com S 4 Credit The gradient Vertical ÷ Horizontal The gradient from Coordinates Drawing Straight line graphs General Equation y = mx + c Equation from 2 Points Modelling Situations Best – fitting straight line Exam Type Questions

Starter Questions www. mathsrevision. com S 4 Credit Q 1. Calculate 7 – 5 x 2 Q 2. Calculate Q 3. Is this triangle right angled ? Explain 9 8 5 19 -Oct-21 Created by Mr. Lafferty Maths Dept

The Gradient of a Line www. mathsrevision. com S 4 Credit Learning Intention Success Criteria 1. To show to get the equations for horizontal and vertical lines. 1. Understand that vertical lines have equations of the form x = a 2. Understand that horizontal lines have equations of the form y = a 19 -Oct-21 Created by Mr. Lafferty Maths Dept

Equations for Vertical and Horizontal lines y x = -6 10 9 8 7 6 5 4 3 2 1 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 19 -Oct-21 1 2 3 4 5 6 7 8 9 Mark the points on your grid below and then join them together Vertical lines have equations of the form 10 x x= 8 Horizontal lines have equations of the form y= 2 y = -9 Created by Mr. Lafferty Maths Dept

The Gradient www. mathsrevision. com S 4 Credit Now Try MIA Exercise 2. 1 Ch 7 (page 136) 19 -Oct-21 Created by Mr. Lafferty Maths Dept

Starter Questions www. mathsrevision. com S 4 Credit Q 1. Write this number in full to 1 sig. figs Q 2. Calculate the volume of the triangular prism. 20 cm 12 cm 8 cm 19 -Oct-21 Created by Mr. Lafferty Maths Dept

The Gradient of a Line www. mathsrevision. com S 4 Credit Learning Intention Success Criteria 1. To explain how to calculate the gradient using a right angle triangle 1. Gradient is : change in vertical height divided by change in horizontal distance 2. Calculate simple gradients. 19 -Oct-21 Created by Mr. Lafferty Maths Dept

The Gradient Difference in y -coordinates www. mathsrevision. com S 4 Credit The gradient is the measure of steepness of a line Change in vertical height Change in horizontal distance The steeper a line the bigger the. Difference gradient in x -coordinates 19 -Oct-21 Created by Mr. Lafferty Maths Dept

The Gradient S 4 Credit www. mathsrevision. com 3 4 3 2 3 5 2 19 -Oct-21 Created by Mr. Lafferty Maths Dept 6

The Gradient www. mathsrevision. com S 4 Credit Now Try MIA Exercise 3. 1 Ch 7 (page 139) 19 -Oct-21 Created by Mr. Lafferty Maths Dept

Starter Questions www. mathsrevision. com S 4 Credit Q 1. A house is valued at £ 50 000. Calculate it’s value after 4 years if it appreciates by 5% each year. Q 2. Calculate 3. 36 x 70 to 2 significant figures. Q 3. Calculate the volume of a cylinder with radius 5 cm and height 100 cm. 19 -Oct-21 Created by Mr. Lafferty Maths Dept

The Gradient of a Line www. mathsrevision. com S 4 Credit Learning Intention Success Criteria 1. To explain positive and negative gradients using coordinates. 19 -Oct-21 1. Know gradient formula. 2. Calculate gradients given two coordinates. Created by Mr. Lafferty Maths Dept

The gradient using coordinates www. mathsrevision. com S 4 Credit m = gradient y-axis y 2 y 1 O 19 -Oct-21 x 1 x-axis x 2 www. mathsrevision. com 13

The gradient using coordinates S 4 Credit www. mathsrevision. com Find the gradient of the line. y-axis O 19 -Oct-21 m = gradient x-axis www. mathsrevision. com 14

The gradient using coordinates S 4 Credit Find the gradient of the two lines. y-axis O 19 -Oct-21 www. mathsrevision. com x-axis 15

The gradient using coordinates www. mathsrevision. com S 4 Credit The gradient formula is : It is a measure of how steep a line is A line sloping up from left to right is a positive gradient A line sloping down from left to right is a negative gradient 19 -Oct-21 Created by Mr. Lafferty Maths Dept

The gradient using coordinates www. mathsrevision. com S 4 Credit Now try MIA Ex 4. 2 Ch 7 (page 143) 19 -Oct-21 Created by Mr. Lafferty Maths Dept

Straight Line Graphs www. mathsrevision. com S 4 Credit Learning Intention Success Criteria 1. To draw graphs by using a coordinate table 1. Understand the keypoints of drawing a straight line graph 2. Be able to plot a straight line graph 19 -Oct-21 Created by Mr. Lafferty Maths Dept

Drawing Straight Line Graphs y = ax + b y y=x 10 y = 3 x+1 9 8 x -2 0 2 7 x 0 3 -4 y 0 3 -4 6 y -5 1 7 5 4 3 2 1 -10 -9 y=x-3 x 0 4 8 y -3 1 5 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 19 -Oct-21 Created by Mr. Lafferty Maths Dept 8 9 10 x y = 2 x x 0 3 -4 y 6 -8 0

Straight Line Graphs www. mathsrevision. com S 4 Credit Key Points 1. Make a table 2. Calculate and plot 3 coordinates 3. Draw a line through points 19 -Oct-21 Created by Mr. Lafferty Maths Dept

Straight Line Graphs www. mathsrevision. com S 4 Credit Now try MIA Ex 5. 1 Q 5 Only Ch 7 (page 145) 19 -Oct-21 Created by Mr. Lafferty Maths Dept

Starter Questions www. mathsrevision. com S 4 Credit Q 1. Write out in full to 2 sig. figs. Q 2. A superstore make 20% profit on each can of soup they sell. If they buy in a can for 50 p. What is the selling price. Q 3. A hemisphere has a diameter of 10 cm. Calculate its volume. 19 -Oct-21 Created by Mr. Lafferty Maths Dept

The Straight Line Equation www. mathsrevision. com S 4 Credit Learning Intention Success Criteria 1. To explain the connection between the straight line equation and the gradient. 19 -Oct-21 1. Understand the term standard form. 2. Identity the gradient m from the standard form. Created by Mr. Lafferty Maths Dept

Straight line equation and the gradient connection y 10 y = 2 x - 5 x 9 1 3 7 y -5 -3 1 5 0 y = 2 x + 1 8 6 4 x 0 1 3 y 3 7 1 3 2 1 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 x -1 -2 -3 -4 -5 m=2 -6 -7 -8 -9 -10 19 -Oct-21 Created by Mr. Lafferty Maths Dept m=2

Straight Line Equation y S 4 Credit www. mathsrevision. com All straight lines have the equation of the form lines are parallel if they have the same gradient Where line Gradient meets y-axis y = mx + c 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 x Find the equations of the following lines y = x 19 -Oct-21 y = x+4 y = 4 x+2 Created by Mr. Lafferty Maths Dept y = -0. 5 x+2

The Gradient of a Line www. mathsrevision. com S 4 Credit Now try MIA Ex 6. 1 Ch 7 (page 146) 19 -Oct-21 Created by Mr. Lafferty Maths Dept

Starter Questions www. mathsrevision. com S 4 Credit Q 1. Write out in full to 1 significant fig. Q 2. A computer store buys in a laptop for £ 500. They want to make a 40% profit. How much do they sell it for. Q 3. A line is parallel to y = 2 x. Write down its equation 19 -Oct-21 Created by Mr. Lafferty Maths Dept

lines are parallel if. Straight same gradient S 4 Credit Line Equation www. mathsrevision. com All straight lines have the equation of the form y = mx + c Slope left to right upwards positive gradient Gradient Slope left to right downwards negative 19 -Oct-21 gradient y - intercept Created by Mr. Lafferty Maths Dept y intercept is were line cuts y axis

Equation of a Straight Line y = mx+c S 4 Credit www. mathsrevision. com To find the equation of a straight line we need to know Two points that lie on the line ( x 1, y 1) and ( x 2, y 2) Or The gradient and a point on the line m and (a, b) 19 -Oct-21 www. mathsrevision. com

Equation of a Straight Line y = mx+c www. mathsrevision. com S 4 Credit Find the equation of the straight line passing through the points (4, 4) and (8, 24). Solution Using the point (4, 4) and the gradient m = 5 sub into straight line equation y = mx + c 4 = 5 x 4 + c Equation : y = 5 x - 16 c = 4 - 20 = -16

Equation of a Straight Line y = mx+c www. mathsrevision. com S 4 Credit Find the equation of the straight line passing through the points (3, -5) and (6, 4). Solution Using the point (6, 4) and the gradient m = 3 sub into straight line equation y = mx + c 4 = 3 x 6 + c Equation : y = 3 x - 14 c = 4 - 18 = -14

Straight Line Graphs www. mathsrevision. com S 4 Credit Now try MIA Ex 6. 2 Ch 7 (page 147 ) 19 -Oct-21 Created by Mr. Lafferty Maths Dept

Starter Questions www. mathsrevision. com S 4 Credit Q 1. The points ( 1, 4) and (3, 11) lie on a line. Find the gradient of the line. Q 2. Complete the table given : x y Q 3. -3 0 3 Are the two lines parallel. Explain answer y=x+2 19 -Oct-21 y = 3 x + 1 and y = 2 x + 2 Created by Mr. Lafferty Maths Dept

Modelling Using Straight Line Equation www. mathsrevision. com S 4 Credit Learning Intention Success Criteria 1. How to model real life situations using straight line theory 1. Be able to work out gradient and y intercept using a graph. 2. Form an equation for any straight line graph. 19 -Oct-21 Created by Mr. Lafferty Maths Dept

Modelling Real – life Pick any 2 points The cost for hiring a plumber per hour is shown below 10 Calculate the gradient. (b) What is the value of C when T = 0 30 (c) Write down an equation connecting C and T. 100 90 Cost £ (a) (7, 100) C 80 70 60 50 40 30 (0, 30) 20 10 C= (d) T + 0 1 2 3 4 6 7 8 9 Time (hours) Find the cost for a plumber for 10 hours? T = 10 5 C = 10 x 10 + 30 = £ 130 10 T

Modelling Real – life Pick any 2 points The graph shows how a the volume of water tank drains over time. -5 Calculate the gradient. (b) What is the value of V when T = 0 80 (c) Write down an equation connecting V and T. 100 (0, 80) 90 Volume (a) V 80 70 60 (8, 40) 50 40 30 20 10 V= (d) 0 T + 1 2 3 4 5 6 7 8 9 10 T Time (mins) How long before the tank is empty? V=0 0 = -5 x. T + 80 T = (-80) ÷(– 5) = 16 mins

Straight Line Equation www. mathsrevision. com S 4 Credit Now try Ex 7. 1 MIA (page 149) 19 -Oct-21 Created by Mr. Lafferty Maths Dept

Starter Questions www. mathsrevision. com S 4 Credit Q 1. The points ( 5, 7) and (7, 21) lie on a line. Find the gradient of the line. Q 2. Complete the table given : x y Q 3. -3 3 Are the two lines parallel. Explain answer y = -2 x + 1 19 -Oct-21 0 y = 2 x + 10 and y = 2 x + 1 Created by Mr. Lafferty Maths Dept

Best Fit Straight Line Equation www. mathsrevision. com S 4 Credit Learning Intention Success Criteria 1. How to model real life situations using straight line theory 1. Be able to work out gradient and y intercept using a graph. 2. Form an equation for any straight line graph. 19 -Oct-21 Created by Mr. Lafferty Maths Dept

Best-Fitting Straight line Data was collected on pupils weight and height. Data is plotted below. (b) 2. 57 c=0 h= (d) w + Height (cms) (a) Pick any Is there correlation between height and weight. 2 points Yes, a positive correlation h 200 Draw in the best-fit line and 180 x (70, 180) 160 find an equation relating 140 height and weight. 120 100 80 60 40 20 (0, 0) 0 x 10 20 30 40 50 60 70 80 90 100 Weight (Kgs) What height is a pupils who weights 40 kgs? w = 40 h = 2. 57 x 40 = 102. 8 cms w

Best-Fitting Straight line A survey was carried out on the value of cars depending on their age The data is plotted below. (b) -1. 25 c = 18 v= (d) value £ ‘ 000 (a) Pick any Is there correlation between value and age. 2 points Yes, a negative correlation v 20 Draw in the best-fit line and 18 x(0, 18) 16 find an equation relating 14 value and year. 12 y+ 10 x (8, 8) 8 6 4 2 0 1 2 3 4 5 6 7 8 9 10 Years What is the cost of a car after 4 years? y=4 v = -1. 25 x 4 + 18 = 13 Value = £ 13 000 y

Best Fit Straight Line Equation www. mathsrevision. com S 4 Credit Now try Ex 8. 1 MIA (page 151) 19 -Oct-21 Created by Mr. Lafferty Maths Dept

Exam Type Straight Line Questions www. mathsrevision. com S 4 Credit a) b) Example The graph shows an electrician’s charging system. He has a call-out charge plus an hourly rate. Work out the equation of the line. Calculate the cost of a 10 hour job.

Exam Type Straight Line Questions www. mathsrevision. com S 4 Credit a) Pick two convenient points on the line, say (0, 30) and (5, 80). Thinking of the form y = mx + c The y-intercept gives c = 30 The equation is: y = 10 x + 30 = 10 The label on the y-axis is C and the label on the x-axis is T So the equation is C = 10 T + 30 b) Find C when T = 10 C = 10 x 10 + 30 = 130 The cost of a 10 hr job is £ 130.

Exam Type Straight Line Questions S 4 Credit www. mathsrevision. com 1. The tank of a car contains 5 litres of petrol. The graph below shows how the volume of petrol in this tank changes as a further 45 litres of petrol is pumped in at a steady rate for 60 seconds. Find the equation of the straight line in terms of V and t.

Exam Type Straight Line Questions S 4 Credit 2. In the diagram below. A is the point (-1, -7) and B is the point (4, 3). (a) Find the gradient of the line AB. (b) AB cuts the y-axis at the point (0, -5). Write down the equation of the line AB. (c) The point (3 k, k) lies on the line AB. Find the value of k.

Exam Type Straight Line Questions www. mathsrevision. com S 4 Credit 3. A water pipe runs between two buildings. These are represented by the points A and B in the diagram below. (a) Using the information in the diagram, show that the equation of the line AB is 3 y – x = 6.

Exam Type Straight Line Questions www. mathsrevision. com S 4 Credit (b) An emergency outlet pipe has to be built across the main pipe. The line representing this outlet pipe has equation 4 y + 5 x = 46. Calculate the coordinates of the point on the diagram at which the outlet pipe will cut across the main water pipe.

Exam Type Straight Line Questions www. mathsrevision. com S 4 Credit