Straight Line Nat 5 www mathsrevision com Simple

Straight Line Nat 5 www. mathsrevision. com Simple Gradient Equation of a line gradient and y-intercept Equation given any two points Straight line in real-life Gradient Revision Higher Form of straight Line y – b = m(x – a) The General Equation of a straight line. Best – fitting straight line Exam Type Questions

Starter Questions www. mathsrevision. com Nat 5 In pairs “Explain the rules for fractions” 10 -Nov-20 Created by Mr. Lafferty Maths Dept

The Gradient of a Line www. mathsrevision. com S 4 Learning Intention Success Criteria 1. We are learning to calculate simple gradient using a right angle triangle 1. Gradient is : change in vertical height divided by change in horizontal distance 2. Calculate simple gradients. 10 -Nov-20 Created by Mr. Lafferty Maths Dept

The Gradient Difference in y -coordinates www. mathsrevision. com S 4 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 10 -Nov-20 Created by Mr. Lafferty Maths Dept

The Gradient S 4 www. mathsrevision. com 3 4 3 2 3 5 2 10 -Nov-20 Created by Mr. Lafferty Maths Dept 6

Straight Line www. mathsrevision. com Nat 5 Now try N 5 TJ Ex 6. 1 Ch 6 (page 50) 10 -Nov-20 Created by Mr. Lafferty Maths Dept

Starter Questions www. mathsrevision. com Nat 5 Q 1. Is this triangle right angled ? Explain 9 8 5 10 -Nov-20 Created by Mr. Lafferty Maths Dept

Straight line www. mathsrevision. com Nat 5 Learning Intention Success Criteria 1. We are learning to find the equation of a straight line. 1. Understand how to calculate the gradient and identify yintercept. 2. Be able to write down equation of a straight line in the format y = mx + c. 10 -Nov-20 Created by Mr. Lafferty Maths Dept

lines are parallel if. Straight Nat 5 same gradient Line Equation www. mathsrevision. com Almost all straight lines have the equation of the form Slope left to right upwards positive gradient y = mx + c Gradient Slope left to right downwards negative 10 -Nov-20 gradient y - intercept Created by Mr. Lafferty Maths Dept y intercept is were line cuts y axis

The gradient using coordinates www. mathsrevision. com Nat 5 m = gradient y-axis y 2 y 1 O 10 -Nov-20 x 1 x-axis x 2 www. mathsrevision. com 10

www. mathsrevision. com Nat 5 Remember The gradient parallel means same gradientusing coordinates 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 10 -Nov-20 Created by Mr. Lafferty Maths Dept

The gradient using coordinates Nat 5 Find the gradient of the two lines. y-axis O 10 -Nov-20 www. mathsrevision. com x-axis 12

The gradient using coordinates Nat 5 Write down the gradient and y intercept for each line. (a) y = -3 x - 5 (b) 4 y - 8 x = 24 m=-3 m=2 c=-5 c=6 Challenge 1 Write the equation given the gradient and y intercept. (a) m = 1. 5 c = 1 y = 1. 5 x + 1 (b) m = -2 y = -2 x - 4 10 -Nov-20 c=-4 www. mathsrevision. com Challenge 2 13

Straight Line www. mathsrevision. com Nat 5 Now try N 5 TJ Ex 6. 2 Ch 6 (page 52) 10 -Nov-20 Created by Mr. Lafferty Maths Dept

Starter Questions www. mathsrevision. com Nat 5 Q 1. A house 4 years ago is valued at £ 50 000. Calculate it’s value if it has increased by 5%. Q 2. Calculate 3. 36 x 70 to 2 significant figures. Q 3. Write down the 3 ways of factorising. 10 -Nov-20 Created by Mr. Lafferty Maths Dept

Straight Line www. mathsrevision. com Nat 5 Learning Intention Success Criteria 1. We are learning to find the equation of a straight line given any two points. 1. Know how to calculate the gradient using formula. 2. Know how to find y-intercept using substitution. Be able to write down straight line equation in y = mx + c format. 10 -Nov-20 Created by Mr. Lafferty Maths Dept

Equation of a Straight Line y = mx + c Nat 5 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) 10 -Nov-20 www. mathsrevision. com We will look at this later

Find the equations of the straight lines below given the coordinates. y (4, 1) and (8, 5) using x y Sub (4, 1) into y = mx + c 1 = 1 x 4 + c c=1 -4 c = -3 y = x -3 10 -Nov-20 -10 (-6, 7) and (-2, 3) x y Sub (-2, 3) into y = mx + c c=3 -2 c=1 y = -x + 1 Demo

Equation of a Straight Line y = mx + c www. mathsrevision. com Nat 5 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

Straight Line www. mathsrevision. com Nat 5 Now try N 5 TJ Ex 6. 3 Ch 6 (page 54) 10 -Nov-20 Created by Mr. Lafferty Maths Dept

Starter Questions www. mathsrevision. com Nat 5 Q 1. The points ( 1, 4) and (3, 11) lie on a line. Find the gradient of the line. Q 2. Are the two lines parallel. Explain your answer y=x+2 10 -Nov-20 and y = 2 x + 2 Created by Mr. Lafferty Maths Dept

Modelling Using Straight Line Equation www. mathsrevision. com Nat 5 Learning Intention Success Criteria 1. We are learning 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. 10 -Nov-20 Created by Mr. Lafferty Maths Dept

Real – Life Straight Line Nat 5 www. mathsrevision. com A LINEAR equation can and is usually written in the form y = mx + c Note : Other letters can be used v = ut + a The following equations are NOT linear Why ? y = mx 2 + c v = ut 2 + a Not allowed powers greater than 1

www. mathsrevision. com Using the table Find the John earns draw a graph of Real-Life £ 2 gradient an hour and P against h Pintercept Nat 5 Write down Straight Line How much dida he formula get connecting paid for P and 48 h. hours. working h 0 1 2 3 P 0 2 4 6 (2, 4) (0, 0) (1, 2) (3, 6) P m =2 c =0 6 5 4 3 P = 2 h 2 P = 2 x 48 1 P = £ 96 0 1 2 3 h

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 V when T = 0 30 (c) Write down an equation connecting V and T. 100 90 Cost £ (a) (7, 100) V 80 70 60 50 40 30 (0, 30) 20 10 V= (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

Real – Life Straight Line www. mathsrevision. com Nat 5 Now try N 5 TJ Ex 6. 4 Ch 6 (page 55) 10 -Nov-20 Created by Mr. Lafferty Maths Dept

Starter Questions www. mathsrevision. com Nat 5 Q 1. Prove that the coordinates ( 1, 1) (2, 2) and (3, 3) lie on the same line. Q 2. Are the two lines parallel. Explain answer y = -4 x + 1 10 -Nov-20 and 6 y - 24 x = 12 Created by Mr. Lafferty Maths Dept

Gradient - Revision www. mathsrevision. com Nat 5 Learning Intention Success Criteria 1. We are revising gradient. 10 -Nov-20 1. Use gradient formula to calculate gradient. Created by Mr. Lafferty Maths Dept

www. mathsrevision. com Nat 5 Remember The gradient parallel means same gradientusing coordinates 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 10 -Nov-20 Created by Mr. Lafferty Maths Dept

Gradient Facts Outcome 1 Higher www. mathsrevision. com Sloping left to right up has +ve gradient m>0 Sloping left to right down has -ve gradient m<0 Horizontal line has zero gradient. m=0 y=c Vertical line has undefined gradient. x=a www. mathsrevision. com 10 -Nov-20 34

Gradient - Revision www. mathsrevision. com Nat 5 Find gradients PQ , QR and RP

Gradient Revision www. mathsrevision. com Nat 5 Now try N 5 TJ Ex 6. 5 Ch 6 (page 58) 10 -Nov-20 Created by Mr. Lafferty Maths Dept

Starter Questions www. mathsrevision. com Nat 5 Q 1. Prove that the coordinates ( 1, 1) (2, 2) and (3, 3) lie on the same line. Q 2. Are the two lines parallel. Explain answer y = -4 x + 1 10 -Nov-20 and 6 y - 24 x = 12 Created by Mr. Lafferty Maths Dept

Higher Form of Straight Line Equation www. mathsrevision. com Nat 5 Learning Intention Success Criteria 1. We are learning alternative way to find straight line equation. 1. Know Nat 5 version of straight line equation y – b = m(x – a) 2. Form an straight equation from information given. 10 -Nov-20 Created by Mr. Lafferty Maths Dept

Equation of a Straight Line y = mx + c Nat 5 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) 10 -Nov-20 www. mathsrevision. com

The Equation of the Straight Line y – b = m (x - a) Nat 5 Demo www. mathsrevision. com The equation of any line can be found if we know the gradient and one point on the line. y P (x, y) y m b O A (a, b) m= y -- bb xx –- aa a x x Gradient, y–b=m(x–a) m y-b (x – a) Point (a, b) Point on the line ( a, b )

Equation of a Straight Line y - b = m(x – a) www. mathsrevision. com Nat 5 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 – b = m(x - a) y – 4 = 3(x - 6) Equation : y = 3 x - 14 OR y – (-5) = 3(x - 3) Equation : y = 3 x - 14

Real – Life Straight Line www. mathsrevision. com Nat 5 Now try N 5 TJ Ex 6. 6 Ch 6 (page 59) 10 -Nov-20 Created by Mr. Lafferty Maths Dept

Starter Questions www. mathsrevision. com Nat 5 Q 1. Find the equation of the straight line passing through and (4, 5) and parallel to the line 2 x + y = 1 Q 2. Expand (x - 2)(x 2 + 3 x + 1) 10 -Nov-20 Created by Mr. Lafferty Maths Dept

General Equation of a Straight Line www. mathsrevision. com Nat 5 Learning Intention Success Criteria 1. We are learning the general form for a straight line. 1. Know the format for the general form of a straight line. 2. Be able to rearrange general form. 10 -Nov-20 Created by Mr. Lafferty Maths Dept

Straight Line Facts www. mathsrevision. com Nat 5 Another version of the straight line general formula is: ax + by + c = 0 You need to be able to arrange this form to identify Key information i. e. Gradient and y–intercept. Demo

Nat 5 Simultaneous Equations Straight Lines www. mathsrevision. com Find the gradient and y-intercept for equations below x - y – 4 = 0 and 4 x + 2 y + 12 = 0 Rearrange ( BALANCING METHOD) x – y – 4 = 0 y=x-4 m=1 c=-4 Rearrange ( BALANCING METHOD) 4 x + 2 y + 12 = 0 y = -2 x - 3 10 -Nov-20 m = -2 c=-6 Created by Mr. Lafferty Maths Department

Real – Life Straight Line www. mathsrevision. com Nat 5 Now try N 5 TJ Ex 6. 7 Ch 6 (page 61) 10 -Nov-20 Created by Mr. Lafferty Maths Dept

Starter Questions www. mathsrevision. com Nat 5 Q 1. The points ( 5, 7) and (7, 21) lie on the same line. Find the gradient of the line. Q 2. Are the two lines parallel. Explain answer y = -2 x + 1 10 -Nov-20 and y = 2 x + 1 Created by Mr. Lafferty Maths Dept

Best Fit Straight Line Equation www. mathsrevision. com Nat 5 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. 10 -Nov-20 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 Nat 5 Now try Sheet provided 10 -Nov-20 Created by Mr. Lafferty Maths Dept