Slope & y-intercept of a Line

Since, we have already discussed the slope intercept form of the equation of a line; we will now learn how to find the slope & y-intercept for any given equation of line.

Recall that, the length of the intercept made by of a line on the Y-axis is called its y-intercept & using Slope Intercept form the equation of a line with slope or gradient m and making an y-intercept of c units is given by y = mx + c.

If the equation of the given line is a x + by + d = 0.

We rewrite the given equation in the slope intercept form by taking the term containing, x & constant, d on the other side of the equation i.e. by = – a x – d or y = $\frac{-a}{b}$ $\times$ – d or y = $\frac{-a}{b}$ $\times$ + $\frac{-d}{b}$

& then compare this with y = mx + c we have slope m = $\frac{-a}{b}$ & y intercept c= $\frac{-d}{b}$

Let us take a few examples

Example:

Find the slope & y-intercept of the line x+y=7.Here, we can rewrite the equation as y = – x + 7 = (-1)x + 7.Hence here slope m = (-1) & y-intercept, c = 7.
Find the slope & y-intercept of the line 4x + 2y = 8.Here, we can rewrite the equation as 2y = – 4x + 8 = (-4)x + 8.or y = (-2)x + 4.Hence here slope m = (-2) & y-intercept, c = 4.
Find the slope & y-intercept of the line 7x + 8y – 15 = 0.Here, we can rewrite the equation as 8y = –7x + 15 = (-7)x + (15). y= $\frac{-7}{8}$ & y-intercept, c = $\frac{15}{8}$ .Hence here slope m = $\frac{-7}{8}$ & y-intercept, c= $\frac{15}{8}$ .
Here, we can rewrite the equation as y = (0)x + 0.Hence here slope, m = 0 & y-intercept, c = 0.Find the slope & y-intercept of the line y = 0.