Equations of a straight line

MTH 101: Equation of Straight Line
University of Benin (UNIBEN)
Study guide
Simplified questions and answers

1. Find the equation of a line passing through (3, -5) and (-7, 2) in the form ax + by + c =0 where
a, b, c are all integers

Answer
If you have (x1, y1) = (3, -5) and (x2, y2) = (-7, 2), First find the gradient for the points using the
gradient equation,
m = y2 – y1
x2 – x1
m = 2 – (-5)
-7 – 3
7
m=
−10
using the y-y1 = m (x- x1) form of equation, we now have
7
y – (-5) = (x – 3)
−10

7 x−21
=y+5=
−10
Cross Multiply to remove the fraction

7x – 21 = -10y – 50
Writing the equation in the form of ax + by + c =0,
7x – 21 + 10y + 50 = 0
Collecting like terms
7x + 10y + 50– 21 = 0
7x + 10y + 29 = 0
2. A straight line has gradient 2 and crosses the y-axis at the point (0, -4) write down the equation
of the line
Answer
The line crosses the y axis at (0, -4) so the y intercept is -4
i.e. c = -4
the gradient of the line is 2, so m = 2
Using the equation y = mx + c and substituting the given values into the equation,
Therefore,