# What is the slope intercept form of the line passing through (3,2)  with a slope of 7/5 ?

Jun 14, 2018

$y = \frac{7}{5} x - \frac{11}{5}$

#### Explanation:

First use the Point Slope form of a line:

$\left(y - \textcolor{b l u e}{{y}_{1}}\right) = \textcolor{g r e e n}{m} \left(x - \textcolor{b l u e}{{x}_{1}}\right)$

$\left(y - \textcolor{b l u e}{2}\right) = \textcolor{g r e e n}{\frac{7}{5}} \left(x - \textcolor{b l u e}{3}\right)$

Now do the algebra to convert it to slope intercept form:

$y - 2 = \frac{7}{5} x - \frac{21}{5}$

$y = \frac{7}{5} x - \frac{21}{5} + 2$

$y = \frac{7}{5} x - \frac{21}{5} + \frac{10}{5}$

$y = \frac{7}{5} x - \frac{11}{5}$

graph{y-2=7/5x-21/5 [-10, 10, -5, 5]}

Jun 14, 2018

$y = \frac{7}{5} x - \frac{11}{5}$

#### Explanation:

$\text{the equation of a line in "color(blue)"slope-intercept form}$ is.

•color(white)(x)y=mx+b

$\text{where m is the slope and b the y-intercept}$

$\text{here } m = \frac{7}{5}$

$y = \frac{7}{5} x + b \leftarrow \textcolor{b l u e}{\text{is the partial equation}}$

$\text{to find b substitute "(3,2)" into the partial equation}$

$2 = \frac{21}{5} + b \Rightarrow b = \frac{10}{5} - \frac{21}{5} = - \frac{11}{5}$

$y = \frac{7}{5} x - \frac{11}{5} \leftarrow \textcolor{red}{\text{in slope-intercept form}}$