# What is the slope intercept form for a line containing the points (10, 15) and (12, 20)?

Mar 24, 2018

$y = \frac{2}{5} \cdot x + 11$

#### Explanation:

Given:
Point 1 : (10,15)
Point 2: (12,20)

The Slope-Intercept form is y = mx + b;
Slope (m) = $\frac{{x}_{2} - {x}_{1}}{{y}_{2} - {y}_{1}}$
m = $\frac{12 - 10}{20 - 15}$ = $\frac{2}{5}$

Therefore, y = $\frac{2}{5}$x + b.
Now, plug any one of the above points in this equation to get the y-intercept.

Using Point 1: (10,15);
15 = $\frac{2}{\cancel{5}} \cdot \cancel{10}$ + b
15 = 4 + b

$\therefore$ b = 11
Therefore, the Slope-Intercept form for the above points is $\textcolor{red}{y = \frac{2}{5} \cdot x + 11}$