Plotting Straight-Line Graphs

Mathematics · Algebra · ages 12-14

Name ______________________ Date ____________

A table of values is being built for the line y = 5x. What is y when x is -2?
Answer: ______________
Lena is plotting the line y = 2x + 3. She makes a table of values. What is y when x = 4?
Answer: ______________
For y = x + 3, what is y when x = 2?
- 5
- 6
- 2
The gradient of a line tells you how steep it is.
Circle one: True False
A straight line passes through the points (1, 2) and (5, 10). What is the gradient of the line?
Answer: ______________
Rearrange x + 2y = 8 into the form y = mx + c.
- y = (1/2)x + 4
- y = -(1/2)x + 8
- y = -2x + 4
- y = -(1/2)x + 4
Rearrange the equation 2x + 3y = 12 so it is in the form y = mx + c.
- y = (2/3)x + 4
- y = -(2/3)x + 4
- y = -(2/3)x + 12
- y = -(3/2)x + 4
Find the gradient between the points (2, 4) and (5, 10).
Answer: ______________
A student says their table for y = 3x + 2 gives y = 3 when x = 1. What did they do wrong?
- They used the wrong equation
- They didn't make a mistake
- They forgot to multiply x by 3 before adding 2
Which of these equations has a gradient of -3?
- y = -3x + 2
- y = 3x - 2
- y = 2x - 3
- y = 2x + 3

Answer key

For grown-ups. Fold this page away before handing over the rest.

-10 · Multiplying 5 by -2 gives -10.
11 · Substitute x = 4 into y = 2x + 3 to get 11.
5 · Substitute x = 2 into y = x + 3: 2 + 3 = 5.
True · A bigger gradient, ignoring its sign, means a steeper line.
2 · Rise is 10 - 2 = 8 and run is 5 - 1 = 4, so the gradient is 8 divided by 4, which is 2.
y = -(1/2)x + 4 · Subtract x, then divide by 2 to get y = -(1/2)x + 4.
y = -(2/3)x + 4 · Subtract 2x, then divide every term by 3 to get y = -(2/3)x + 4.
2 · Rise = 10 - 4 = 6. Run = 5 - 2 = 3. Gradient = 6 / 3 = 2.
They forgot to multiply x by 3 before adding 2 · 3(1) + 2 = 5, not 3. They must have skipped the multiplication step and just added 1 + 2.
y = -3x + 2 · In y = mx + c, m is the gradient, and only y = -3x + 2 has m = -3.