Straight Line Graphs www mathsrevision com Int 2

Straight Line Graphs www. mathsrevision. com Int 2 Drawing Straight line graphs The gradient from coordinates The y intercept y = mx + c Other forms / rearranging equation 09 -Sep-21 Created by Mr. Lafferty Maths Dept

Starter Questions www. mathsrevision. com Int 2 Q 1. A house is valued at £ 50 000. Calculate its 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. 09 -Sep-21 Created by Mr. Lafferty Maths Dept

Straight Line Graphs www. mathsrevision. com Int 2 Learning Intention Success Criteria 1. To draw graphs by using a coordinate table 1. Understand the key points of drawing a straight line graph 2. Be able to plot a straight line graph 09 -Sep-21 Created by Mr. Lafferty Maths Dept

Drawing Straight Line Graphs y = mx + c 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 09 -Sep-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 Int 2 Key Points 1. Make a table 2. Calculate and plot 3 coordinates 3. Draw a line through points 09 -Sep-21 Created by Mr. Lafferty Maths Dept

Straight Line Graphs www. mathsrevision. com Int 2 Now try Exercise 1 Odd numbers MIA (page 33) 09 -Sep-21 Created by Mr. Lafferty Maths Dept

Starter Questions www. mathsrevision. com Int 2 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 09 -Sep-21 Created by Mr. Lafferty Maths Dept

The Gradient of a Line www. mathsrevision. com Int 2 Learning Intention Success Criteria 1. To explain how to calculate the gradient using right angled triangles 1. Gradient is : change in vertical height divided by change in horizontal distance 2. Calculate simple gradients. 09 -Sep-21 Created by Mr. Lafferty Maths Dept

The Gradient Difference in www. mathsrevision. com Int 2 y -coordinates 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 09 -Sep-21 Created by Mr. Lafferty Maths Dept

The Gradient www. mathsrevision. com Int 2 m= V = 3 4 H 3 m= V = 2 H 3 m= V = 5 H 2 09 -Sep-21 Created by Mr. Lafferty Maths Dept m= V = 6 H

The Gradient www. mathsrevision. com Int 2 Round the class Exercise 2 MIA (page 36) 09 -Sep-21 Created by Mr. Lafferty Maths Dept

The Gradient of a Line www. mathsrevision. com Int 2 Learning Intention Success Criteria 1. To explain positive and negative gradients using coordinates. 09 -Sep-21 1. Know gradient formula. 2. Calculate gradients given two coordinates. Created by Mr. Lafferty Maths Dept

The gradient using coordinates www. mathsrevision. com Int 2 m = gradient y-axis m = Y 2 – Y 1 X 2 – X 1 y 2 y 1 O 09 -Sep-21 x 1 x-axis x 2 www. mathsrevision. com 13

The gradient using coordinates Int 2 www. mathsrevision. com Find the gradient of the line. y-axis m = gradient m = Y 2 – Y 1 X 2 – X 1 m = 10 – 4 5– 2 O 09 -Sep-21 x-axis www. mathsrevision. com m= 6 = 2 3 14

The gradient using coordinates Int 2 Find the gradient of the two lines. y-axis m = Y 2 – Y 1 m= 8– 2 m= 8 -2 X 2 – X 1 3 -1 -3 – (-1) m = 6 = -3 -2 09 -Sep-21 O www. mathsrevision. com x-axis m= 6 =3 2 15

The gradient using coordinates www. mathsrevision. com Int 2 The gradient formula is : Gradient = m = (y 2 – y 1) (x 2 – x 1) 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 09 -Sep-21 Created by Mr. Lafferty Maths Dept

The gradient using coordinates www. mathsrevision. com Int 2 Exercise 3 Q 1 – Q 3 MIA (page 37) 09 -Sep-21 Created by Mr. Lafferty Maths Dept

Starter Questions www. mathsrevision. com Int 2 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. 09 -Sep-21 Created by Mr. Lafferty Maths Dept

The Gradient of a Line www. mathsrevision. com Int 2 Learning Intention Success Criteria 1. To explain the connection between the straight line equation and the gradient. 09 -Sep-21 1. Understand the term standard form. 2. Identify the gradient m from the standard form. Created by Mr. Lafferty Maths Dept

Straight line equation and the gradient connection y 10 y = -x - 5 x 0 1 9 y = 2 x + 1 8 7 3 6 y -5 -6 -8 5 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 = -1 -6 -7 -8 -9 -10 09 -Sep-21 Created by Mr. Lafferty Maths Dept m=2

Straight Line Equation S 4 Credit www. mathsrevision. com All straight lines have the equation of the form y = mx + c Let’s investigate properties (You need Geo. Gebra to run link) 09 -Sep-21 Created by Mr. Lafferty Maths Dept

Straight Line Equation y 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 09 -Sep-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 Int 2 Now try Exercise 3 Q 4 – Q 9 MIA (page 38) 09 -Sep-21 Created by Mr. Lafferty Maths Dept

Starter Questions www. mathsrevision. com Int 2 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 09 -Sep-21 Created by Mr. Lafferty Maths Dept

lines are parallel if. Straight same gradient 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 09 -Sep-21 gradient y - intercept Created by Mr. Lafferty Maths Dept y intercept is were line cuts y axis

Straight Line Graphs www. mathsrevision. com Int 2 Now try Exercise 4 MIA (page 41 ) 09 -Sep-21 Created by Mr. Lafferty Maths Dept

Starter Questions www. mathsrevision. com Int 2 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 09 -Sep-21 y = 3 x+1 and y = 2 x + 2 Created by Mr. Lafferty Maths Dept

Straight Line Equation www. mathsrevision. com Int 2 Learning Intention Success Criteria 1. To show to rearrange straight line equations into standard form and then identify the gradient and the y - intercept. 1. Be able to rearrange straight line equations. y = mx + c 2. Identify the gradient m and y – intercept c from the standard form. y = mx + c 09 -Sep-21 Created by Mr. Lafferty Maths Dept

www. mathsrevision. com Straight Line Equation This is called the standard All straight lines have an equation of the form y = mx + c Gradient Where line meets y-axis If two lines have the same gradient they are parallel. y = 2 x 09 -Sep-21 y = 2 x+4 Created by Mr. Lafferty Maths Dept

www. mathsrevision. com Just a bit of Straight algebra Line Equation Rearrange the following straight line equations into standard form and identify the gradient and y-intercept. Standard form m c y = 3 x + 4 3 4 2 y – 2 x = 6 y =x+3 1 3 y–x+5=0 y=x-5 1 -5 y=2 0 2 y – 3 x = 4 4 y – 8 = 0 09 -Sep-21 Created by Mr. Lafferty Maths Dept

Straight Line Equation www. mathsrevision. com Find the a line parallel to y – x = 0 and passing through (0, 3). Standard form x–y=0 y =x m c 1 0 A line parallel to y = x has same gradient therefore m = 1 Since it passes through (0, 3) then c = 3 Using standard form line is 09 -Sep-21 y=x+3 Created by Mr. Lafferty Maths Dept

Straight Line Equation www. mathsrevision. com Int 2 Now try Ex 5 MIA (page 45) 09 -Sep-21 Created by Mr. Lafferty Maths Dept