Forms of the Equation of a Straight Line

Mathematics · Geometry · ages 16-17

Name ______________________ Date ____________

Where does the line 3x - 5y + 15 = 0 cross the x-axis?
- (5, 0)
- (-5, 0)
- (0, 3)
- (0, -3)
What is the gradient of the line through (1, 3) and (5, 11)?
Answer: ______________
Where does the line y = 2x - 6 cross the x-axis?
- (0, -6)
- (-3, 0)
- (3, 0)
- (6, 0)
A line has gradient 3 and crosses the y-axis at 8. What is its equation?
- y = 3x + 8
- y = 8x + 3
- y = 3x - 8
- y = 3(x - 8)
y - 2 = 5(x + 3) is written in point-gradient form. Which point does the line pass through?
- (3, 2)
- (2, -3)
- (-3, 2)
- (-3, 5)
The line 6x + 2y - 5 = 0 has gradient -3.
Circle one: True False
Rewrite 4x - 2y + 6 = 0 in the form y = mx + c. What is the gradient?
Answer: ______________
The line through (2, 5) and (2, 9) has gradient 2.
Circle one: True False
A line has gradient 3/4 and passes through (8, 3). At what value of x does it cross the x-axis?
Answer: ______________
Tom works out the gradient through (1, 6) and (4, 0) as (4 - 1) / (0 - 6), which is -1/2. Where is the slip?
- he subtracted the coordinates in opposite orders
- the gradient is always positive between two such points
- he divided the change in x by the change in y, so the gradient is -2
- the two points give no gradient at all

Answer key

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

(-5, 0) · Set y = 0: 3x + 15 = 0, so 3x = -15 and x = -5. The crossing is (-5, 0).
2 · Divide the change in y by the change in x: (11 - 3) / (5 - 1) = 8 / 4 = 2.
(3, 0) · Every point on the x-axis has y = 0. Setting 2x - 6 = 0 gives x = 3, so the crossing is (3, 0).
y = 3x + 8 · The gradient is m and the y-axis crossing is c, so m = 3 and c = 8 give y = 3x + 8.
(-3, 2) · The form is y - y₁ = m(x - x₁), so y₁ = 2. The bracket reads x + 3, which is x - (-3), so x₁ = -3 and the point is (-3, 2).
True · Rearranging gives 2y = -6x + 5, so y = -3x + 2.5 and the gradient is -3.
2 · Move the y term across: 2y = 4x + 6. Dividing by 2 gives y = 2x + 3, so the gradient is 2.
False · Both points have x = 2, so the change in x is 0 and the division cannot be done. This is the vertical line x = 2, which has no gradient.
4 · From y - 3 = (3/4)(x - 8), setting y = 0 gives -3 = (3/4)(x - 8), so x - 8 = -4 and x = 4.
he divided the change in x by the change in y, so the gradient is -2 · The gradient is the change in y over the change in x, not the other way round. That is (0 - 6) / (4 - 1) = -6 / 3 = -2.