Straight Line www mathsrevision com Level 4 Simple

Straight Line www. mathsrevision. com Level 4+ Simple Gradient using Coordinates. Drawing straight lines of the form y = mx + c Finding the Straight Line equation

Starter Questions www. mathsrevision. com Level 4+ In pairs “Explain the rules for fractions” 24 -Feb-21 Created by Mr. Lafferty Maths Dept

The Gradient of a Line www. mathsrevision. com Level 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. 24 -Feb-21 Created by Mr. Lafferty Maths Dept

The Gradient Difference in y -coordinates www. mathsrevision. com Level 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 24 -Feb-21 Created by Mr. Lafferty Maths Dept

The Gradient Level 4+ www. mathsrevision. com 3 4 3 2 3 5 2 24 -Feb-21 Created by Mr. Lafferty Maths Dept 6

Gradient Upwards positive gradient m= 5 4 5 Calculate the gradient thedownhill uphill section ofofthe section m=- 5 4 4 Downwards negative gradient

Straight Line www. mathsrevision. com Level 4+ Now try TJ 4+ Ex 8. 1 Ch 8 (page 46) 24 -Feb-21 Created by Mr. Lafferty Maths Dept

Starter Questions www. mathsrevision. com Level 4+ Q 1. Is this triangle right angled ? Explain 9 8 5 24 -Feb-21 Created by Mr. Lafferty Maths Dept

Straight line www. mathsrevision. com Level 4+ Learning Intention Success Criteria 1. We are learning to find the gradient of a straight line using coordinates. 24 -Feb-21 1. Understand how to calculate the gradient using coordinates. Created by Mr. Lafferty Maths Dept

The gradient using coordinates www. mathsrevision. com Level 4+ m = gradient y-axis y 2 y 1 O 24 -Feb-21 x 1 x-axis x 2 www. mathsrevision. com 10

Remember The gradient parallel means same gradientusing coordinates www. mathsrevision. com Level 4+ 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 24 -Feb-21 Created by Mr. Lafferty Maths Dept

The gradient using coordinates Level 4+ Find the gradient of the two lines. y-axis O 24 -Feb-21 www. mathsrevision. com x-axis 12

Gradient Calculate the gradient for each side of the kite. m=½ (1, 5) (3, 6) Kite m=-½ (5, 5) m = -2 m=2 (3, 1)

Gradient Calculate the gradient for each side of the parallelogram. Parallelogram (3, 6) m=0 (7, 6) m= m= (1, 1) m=0 (5, 1)

Straight Line www. mathsrevision. com Level 4+ Now try TJ 4+ Ex 8. 2 Ch 8 (page 48) 24 -Feb-21 Created by Mr. Lafferty Maths Dept

Starter Questions www. mathsrevision. com Level 4+ 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. 24 -Feb-21 Created by Mr. Lafferty Maths Dept

Straight Line www. mathsrevision. com Level 4+ Learning Intention Success Criteria 1. We are learning to draw and identify straight lines. 1. Create table of values. 2. Draw a straight line. 24 -Feb-21 Created by Mr. Lafferty Maths Dept

Drawing Straight Line Graphs y = mx y y=x 10 y = -3 x 9 8 x 0 2 7 y 0 -3 -6 5 1 x 0 2 6 y 0 2 6 6 4 3 2 1 -10 -9 -8 -7 -6 -5 y = -4 x x y 0 1 2 0 -4 -8 -4 -3 -2 -1 0 1 2 3 4 5 6 7 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 24 -Feb-21 Created by Mr. Lafferty Maths Dept 8 9 10 x y = 2 x x 0 3 4 y 0 6 8

Drawing Straight Line Graphs y = mx + c y y=x 10 y = -3 x+1 9 8 x 0 2 7 y 1 -2 -5 5 1 x 0 2 4 y 0 2 4 6 4 3 2 1 -10 -9 y = -x - 3 x y 0 2 4 -3 -5 -7 -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 24 -Feb-21 Created by Mr. Lafferty Maths Dept 8 9 10 x y = 2 x + 3 x 0 1 2 y 3 5 7

Straight Line www. mathsrevision. com Level 4+ Now try TJ 4+ Ex 8. 3 Ch 8 (page 50) 24 -Feb-21 Created by Mr. Lafferty Maths Dept

Starter Questions www. mathsrevision. com Level 4+ Expand simplify 4( 3 + 2 x) – 3(x + 1) 24 -Feb-21 Created by Mr. Lafferty Maths Dept

lines are parallel if. Straight same gradient Level 4+ 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 24 -Feb-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 Level 4+ 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) 24 -Feb-21 www. mathsrevision. com We will look at this later

The gradient using coordinates Level 4+ www. mathsrevision. com 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 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 24 -Feb-21 c=-4 www. mathsrevision. com 24

Equation of a Straight Line y = mx + c www. mathsrevision. com Level 4+ 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 Level 4+ Now try TJ 4+ Ex 8. 4 Ch 8 (page 51) 24 -Feb-21 Created by Mr. Lafferty Maths Dept