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 \(x= 4\).