# What is the slope intercept form of the line passing through (2,-3)  with a slope of 3/2 ?

Dec 13, 2015

$y = \frac{3}{2} x + \frac{13}{2}$

#### Explanation:

Given:

Point: $\left(2 , - 3\right)$

Slope: $\frac{3}{2}$

You can use the point-slope form: $y - {y}_{0} = m \left(x - {x}_{0}\right)$, where $m$ is the slope and $\left({x}_{0} , {y}_{0}\right)$ is a point on the line.

Solution:

$\left[1\right] \text{ } y - {y}_{0} = m \left(x - {x}_{0}\right)$

Substitute the point $\left(2 , - 3\right)$ into $\left({x}_{0} , {y}_{0}\right)$.

$\left[2\right] \text{ } y - 2 = m \left(x + 3\right)$

Substitute the slope $\frac{3}{2}$ into $m$.

$\left[3\right] \text{ } y - 2 = \frac{3}{2} \left(x + 3\right)$

Isolate $y$ so you can express the line in the slope-intercept form: $y = m x + b$

$\left[4\right] \text{ } y = \frac{3}{2} \left(x + 3\right) + 2$

Multiply $\frac{3}{2}$ to $\left(x + 3\right)$.

$\left[5\right] \text{ } y = \frac{3}{2} x + \frac{9}{2} + 2$

$\left[6\right] \text{ } y = \frac{3}{2} x + \frac{9}{2} + \frac{4}{2}$

$\left[7\right] \text{ } \textcolor{b l u e}{y = \frac{3}{2} x + \frac{13}{2}}$