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KS3 · Algebra

KS3.M-A16 Straight Line Graphs: y = mx + c

Calculators not allowed · about 60 minutes

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Plot the point (2, 3) on a coordinate grid. State the coordinates you plotted.

(1)

A line has equation y = 2x + 1. State the gradient and the y-intercept.

(1)

For the line y = -3x + 4, calculate y when x = 0 and when x = 2. Give both values.

(1)

Draw the line y = x - 2 on a grid. Give the coordinates of two points on the line that you would plot.

(1)

The line y = 0.5x + 3 is drawn. What is the y-intercept? Give your answer as a coordinate point.

(1)

A line passes through the points (1, 2) and (3, 6). Calculate the gradient of this line.

(2)

Find the equation of the line with gradient 3 and y-intercept -1. Write your answer in the form y = mx + c.

(2)

A line has equation y = -2x + 5. A second line has equation y = -2x - 1. Explain whether the lines are parallel or not and why.

(2)

The line y = mx + 2 passes through the point (4, 10). Find the value of m.

(2)

A line through (0, -3) and (2, 1) is drawn. Find its equation in the form y = mx + c.

(2)

The graph of a line is shown passing through (1, 4) and (4, 1). Find the equation of the line in the form y = mx + c.

(3)

A straight line passes through points A(-2, 0) and B(2, 4). Work out the equation of the line in the form y = mx + c.

(3)

Given the line y = 4x - 6, a student plots the point (2, 3) and says it lies on the line. Is the student correct? Show your working.

(3)

Mark scheme · KS3.M-A16 Straight Line Graphs: y = mx + c

Question 1

B1 Point correctly plotted at (2, 3) or coordinates stated as (2, 3) cao
Answer: (2, 3)

Question 2

B1 Gradient = 2 and y-intercept = 1 (or stated as (0, 1)) cao
Answer: gradient 2, y-intercept 1

Question 3

B1 y = 4 when x = 0 and y = -2 when x = 2 cao
Answer: y = 4; y = -2

Question 4

B1 Two correct points on the line, e.g. (0, -2) and (2, 0) or equivalent cao
Answer: (0, -2) and (2, 0)

Question 5

B1 y-intercept (0, 3) cao
Answer: (0, 3)

Question 6

M1 Use gradient formula (change in y)/(change in x) = (6 - 2)/(3 - 1) or equivalent
A1 Gradient = 2 cao
Answer: 2

Question 7

M1 Substitute gradient and intercept into y = mx + c form
A1 y = 3x - 1 cao
Answer: y = 3x - 1

Question 8

M1 States that gradients are equal (both -2) or states property of parallel lines
A1 Concludes the lines are parallel because they have the same gradient (different intercepts) cao
Answer: They are parallel because both have gradient -2 (different y-intercepts).

Question 9

M1 Substitute x=4, y=10 into y = mx + 2 leading to 10 = 4m + 2 or equivalent
A1 m = 2 cao
Answer: 2

Question 10

M1 Find gradient: (1 - (-3))/(2 - 0) = 4/2 = 2 or equivalent
A1 y = 2x - 3 cao
Answer: y = 2x - 3

Question 11

M1 Calculate gradient using (1 - 4)/(4 - 1) or (change in y)/(change in x)
M1 Obtain gradient m = -1
A1 Substitute to find c and give equation y = -x + 5 cao
Answer: y = -x + 5

Question 12

M1 Use gradient formula: (4 - 0)/(2 - (-2)) or equivalent
M1 Find gradient m = 1
A1 Substitute to find c = 2 and give equation y = x + 2 cao
Answer: y = x + 2

Question 13

M1 Substitute x = 2 into y = 4x - 6 to find expected y-value or state the check equation y = 4(2) - 6
M1 Obtain y = 8 - 6 = 2 or show arithmetic leading to 2
A1 State that (2, 3) is not on the line because y would be 2, not 3 cao
Answer: No. Substituting x = 2 gives y = 4(2) - 6 = 2, so the point (2, 3) is not on the line.

Straight Line Graphs: y = mx + c - Worksheets, Questions and Revision