Straight lines from equations

Mathematics · Algebra · ages 12-14

Name ______________________ Date ____________

Which equation has a y-intercept of 5?
- y = 5x + 2
- y = 2x + 5
- y = 5x
- y = x + 2
A line has the equation 2x + 3y = 12. What value of y does it cross the y-axis at?
Answer: ______________
In the equation y = mx + c, what does the number m tell you about the graph?
- Where the line crosses the y-axis
- How steep the line is and which way it slopes
- Where the line crosses the x-axis
- How long the line is
In y = mx + c, which letter tells you where the line crosses the y-axis?
- m
- c
- x
Line A has equation y = 2x + 1. Line B has equation y = 5x + 1. Which line is steeper?
- Line A
- Line B
- They are equally steep
A line has the equation 5x + 2y = 20. What is its x-intercept?
Answer: ______________
A line crosses the y-axis at the point (0, -3) and has a gradient of 2. What is the equation of the line?
- y = 2x - 3
- y = -3x + 2
- y = 2x + 3
- y = 3x - 2
True or false: the graph of y = x squared is a straight line.
Circle one: True False
What is the equation of the straight line that passes through (0, 2) and (3, 8)?
- y = 2x + 2
- y = 3x + 2
- y = 6x
- y = 2x + 6
Ben graphs y = -2x + 4. He says the line goes up as it moves right, because the number in front of x is 2. What is his mistake?
- He ignored the negative sign, so the line actually slopes down as x increases
- He used the wrong y-intercept
- He mixed up m and c

Answer key

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

y = 2x + 5 · In y = mx + c, the y-intercept is c. Only y = 2x + 5 has c = 5.
4 · The y-axis is where x is 0, and plugging in x = 0 leaves 3y = 12, so y = 4.
How steep the line is and which way it slopes · m is the gradient. The further m is from 0, the steeper the line, and a negative m makes the line slope downward as you move right.
c · c is the y-intercept, the point where the line crosses the y-axis.
Line B · Line B has the bigger gradient, 5 compared with 2, so it climbs faster and looks steeper.
4 · The x-intercept is where the line crosses the x-axis, which means y = 0. That gives 5x = 20, so x = 4.
y = 2x - 3 · Start from y = mx + c. The gradient gives m = 2, and crossing the y-axis at -3 gives c = -3, so y = 2x - 3.
False · False. Plotting points like (0, 0), (1, 1), (2, 4), and (3, 9) shows the values speeding up, so the graph curves upward instead of forming a straight line.
y = 2x + 2 · The point (0, 2) gives c = 2 directly, and the gradient between the two points is (8 - 2) / (3 - 0) = 2, so the equation is y = 2x + 2.
He ignored the negative sign, so the line actually slopes down as x increases · The gradient here is -2, not 2. A negative gradient means the line slopes down as x increases.