Forms of the Equation of a Straight Line

Mathematics · Geometry · ages 16-17

Name ______________________ Date ____________

Write the line through (9, 11) with gradient 6 in point-gradient form.
- y - 9 = 6(x - 11)
- y - 11 = 6(x - 9)
- y + 11 = 6(x + 9)
- y - 11 = 9(x - 6)
What is the equation of the horizontal line through (4, -6)?
- x = 4
- y = 4
- x = -6
- y = -6
Where does the line 2x + 5y = 10 meet the x-axis? Give the x-coordinate.
Answer: ______________
What is the y-intercept of the line 3x + 4y - 12 = 0?
Answer: ______________
Rewrite 3x + 4y - 12 = 0 in gradient-intercept form. What is its gradient? Give your answer as a decimal.
Answer: ______________
2x + 5y - 10 = 0 and y = -0.4x - 2 are the same line.
Circle one: True False
The line through (2, 5) and (2, 9) has gradient 2.
Circle one: True False
Rewrite 4x - 2y + 6 = 0 in the form y = mx + c. What is the gradient?
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
A line passes through (0, 5) and (10, 0). Which equation describes it?
- x + 2y - 10 = 0
- x - 2y + 10 = 0
- 2x + y - 10 = 0
- x + 2y + 10 = 0

Answer key

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

y - 11 = 6(x - 9) · In y - y₁ = m(x - x₁) the y-coordinate 11 goes with y and the x-coordinate 9 goes with x, and m is 6.
y = -6 · A horizontal line keeps the same height everywhere, so y stays at -6 whatever x does. Its equation is y = -6.
5 · Set y = 0: 2x = 10, so x = 5.
3 · In y = -0.75x + 3 the constant term 3 is the y-intercept.
-0.75 · 4y = -3x + 12 gives y = -0.75x + 3, so the gradient is -0.75.
False · Rearranging the first gives 5y = -2x + 10, so y = -0.4x + 2. The gradient matches but the constant is +2, not -2, so the two are different lines.
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.
2 · Move the y term across: 2y = 4x + 6. Dividing by 2 gives y = 2x + 3, so the gradient is 2.
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.
x + 2y - 10 = 0 · The gradient is (0 - 5) / (10 - 0) = -1/2, so y = -(1/2)x + 5. Multiplying by 2 gives 2y = -x + 10, which tidies to x + 2y - 10 = 0.