Equation of a straight line

The general equation of a straight line is:

y = mx + c

where m is the gradient and c is the y-intercept (where the straight line cuts the y-axis)

Example

Find the gradient and y-intercept for the straight line with equation y = 5x + 7?

Answer

m=5

c=7 so y-intercept is (0, 7)

Try these example questions

Question

Find the gradient and y-intercept for the straight line with equation y = 2x + 3

m = 2

c = 3 so y-intercept is (0, 3).

Question

Find the gradient and y-intercept for the straight line with equation y = 8x - 4

m = 8

c = -4 so y-intercept is (0, -4).

Question

Find the equation of the straight line shown below.

Straight line graph cutting through 3 on the y axis and 6 on the x axis

To find the equation of a straight line we need to know the gradient and the y-intercept.

Looking at the graph, the straight line cuts the y-axis at (0, 3) therefore c = 3.

Remember that the formula to calculate the gradient is:

Gradient(m) = \frac{{vertical\,distance}}{{horizontal\,distance}}

Therefore m = \frac{3}{6} = \frac{1}{2}

Since the straight line shown above is a downward slope, then:

m =  - \frac{1}{2}

So, the equation of the straight line is:

y =  - \frac{1}{2}x + 3

Question

Find the equation of the straight line shown below.

Straight line intercept diagram

y-intercept is (-3, 0) therefore c = -3

m = \frac{v}{h} = \frac{8}{7}

Therefore, the equation of the straight line is:

y = \frac{8}{7}x - 3

Question

Which of these lines in the above diagram are horizontal and which are vertical?

y = 6

x= 3

x = -4

y = -8

Horizontal lines: y =6 and y = -8.

Vertical lines: x=3 and x= 4.