Grade DE Graphs of linear functions Recognise sketch

Grade D/E Graphs of linear functions Recognise, sketch and interpret graphs of linear functions If you have any questions regarding these resources or come across any errors, please contact helpful-report@pixl. org. uk

Key Vocabulary Graph Linear Function Y-intercept Power Gradient Point of intersection Variables

How to recognise linear functions Which of these are linear functions? The power of x 1) y = 12 -5 x is 1 2) y = 3 x + xˉ² 3) y = x³ + 2 x + 5 4) y = 0. 5 x 5) 4 x + 3 y = 6 The power of x is 1 but also -2 By linear we mean that the function must create a straight line graph. The power of x must be 1 The power of x is 1 but also 3 The power of x is 1 Linear equations are generally in the form y=mx + c

How to sketch and interpret linear functions 6) Sketch the function y=4 x+1 labelling the y-intercept. • y=4 x+1 is in the form y=mx+c y= 4 x+1 • We now know that the y-intercept is 1 so the graph goes through the point (0, 1). • As gradient=m=4, we can plot a second point on the line by going one step to the right and 4 steps up from (0, 1). • With two known points on the line, we can sketch the line y=4 x+1 (0, 1)

How to sketch and interpret linear functions 7) Sketch the graph 2 x+5 y=20 labelling the x and y intercept. What does x equal when y=2? You can rearrange the equation; y = -2 x/5 + 4 and then make a table of values to plot the graph. Draw the line y=2 and read off the x-value and the point of intersection x=5

How to sketch and interpret linear functions – Now you try … 1) Sketch the following graphs labelling the y-intercept a) y = -2 x + 7 b) 3 x – 4 y = 18 c) x + y = 4 2) Match each coloured straight line to its corresponding equation A) y = -5 x B) x – y = 3 C) y = 2 x + 1 D)y = 4 x – 8

How to sketch and interpret linear functions – now you try … 1) a) (0, 7) b) c) (0, -4. 5) 2) A) PURPLE B) ORANGE C) GREEN D) BLACK (0, 4)

The graph represents two cars, one blue and one red, coming to rest. a) At what time was the blue car travelling at 10 m/s? b) What is the meaning of the y-intercept for the red car? c) What is the deceleration of the blue car? d) By observing the graph, which car decelerates the fastest and why? Velocity (m/s) Problem Solving and Reasoning Time (s)

Problem Solving and Reasoning velocity c) By observing the graph, which car decelerates the fastest and why? The blue car as it has a steeper gradient d) What is the deceleration of the blue car? Gradient=20/6=3. 33 (3. s. f) Velocity (m/s) The graph represents two cars, one blue and one red, coming to rest. a) At what time was the blue car travelling at 10 m/s? 3 s b) What is the meaning of the y-intercept for the red car? Initial Time (s)

Reason and Explain • Give a example of two variables with a linear relationship • Jack is tracking the growth of her plant. At present the plant has a height of 3 cm. The plant grows at a rate of 2. 5 cm/day. a) Create a linear model to represent the height of the plant after D days. b) What will the plant’s height be after 24?