Algebra · Guided Practice

Straight Line

15 questions with answers and video solutions. Try each one before revealing the answer.

1
The point (2,−3)\displaystyle (2,-3) lies on a straight line with gradient −4\displaystyle -4
Calculate the y\displaystyle y-intercept of this line.

No hints on this one — its full written solution is with the answer.

2
The point (−3,4)\displaystyle (-3,4) lies on a straight line whose y\displaystyle y-intercept is −11\displaystyle -11
Find the gradient of this line and state its equation.

No hints on this one — its full written solution is with the answer.

3
Find the equation of the straight line with gradient 2\displaystyle 2
through the point (3,−1).\displaystyle (3,-1).

No hints on this one — its full written solution is with the answer.

4
Find the equation of the straight line with gradient 34\displaystyle \frac{3}{4} through the point (−2,5)\displaystyle (-2,5)
Give your answer in its simplest form.

No hints on this one — its full written solution is with the answer.

5
Find the equation of the straight line
through (1,7)\displaystyle (1,7) and (−1,3).\displaystyle (-1,3).

No hints on this one — its full written solution is with the answer.

6
Find the equation of the straight line through (−2,5)\displaystyle (-2,5) and (2,−1).\displaystyle (2,-1).

No hints on this one — its full written solution is with the answer.

7
A straight line has equation 3x−7y−4=0.\displaystyle 3x-7y-4=0. Find:
(a)  the gradient
(b)  the point of intersection with the y\displaystyle y-axis
(c)  the point of intersection with the x\displaystyle x-axis.

No hints on this one — its full written solution is with the answer.

8
2014 P1 Q11
(2, 2)4 Marks

(a)  A straight line has equation 4x+3y=12\displaystyle 4x+3y=12.
Find the gradient of this line.

(b)  Find the coordinates of the point where this line crosses the x\displaystyle x-axis.

9
2015 P1 Q8
3 Marks

Find the equation of the line joining the points (−2,5)\displaystyle (-2,5) and (3,15).\displaystyle (3,15).
Give the equation in its simplest form.

10
2017 P2 Q11
2 Marks

A straight line has equation 3x−5y−10=0.\displaystyle 3x-5y-10=0.
Find the gradient of this line.

11
2018 P2 Q14
2 Marks

A straight line has equation 2x−5y=20.\displaystyle 2x-5y=20.
Find the coordinates of the point where this line crosses the y-axis.

12
2021 P2 Q9

A straight line has equation 3x+4y−8=0.\displaystyle 3x+4y-8=0.
(a)  Find the gradient of the line.
(b)  State the coordinates of the point where the line crosses the y\displaystyle y-axis.

No hints on this one — its full written solution is with the answer.

13
2022 P1 Q6
3 Marks

Find the equation of the line passing through the points (−3,−1)\displaystyle (-3,-1) and (−5,7)\displaystyle (-5,7).
Give the equation in its simplest form.

14
2024 P1 Q11
2 Marks

A straight line has equation x+4y−24=0.\displaystyle x+4y-24=0.
Find the gradient of this line.

15
2025 P1 Q6
3 Marks

The diagram shows the straight line passing through points A and B.

Line passing through A(1,12) and B(6,2)

Find the equation of the line AB.
Give the equation in its simplest form.

Keep practising

More straight line questions

New questions, modelled on past paper questions and checked against their marking instructions. Not reprints — you have not seen these before.

Practice questions courtesy of Maths.scot. Full written solutions are on his site — the links above go straight to them.

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