# How do you write the slope intercept form of a line with slope 5/2 passing through (-7,3)?

Dec 20, 2016

$y = \frac{5}{2} x + \frac{41}{2}$

#### Explanation:

First, build the equation using the information given, the slope and a point, using the point-slope formula.

The point-slope formula states: $\textcolor{red}{\left(y - {y}_{1}\right) = m \left(x - {x}_{1}\right)}$
Where $\textcolor{red}{m}$ is the slope and $\textcolor{red}{\left(\left({x}_{1} , {y}_{1}\right)\right)}$ is a point the line passes through.

Substituting the information from the problem gives the equation:

$y - 3 = \frac{5}{2} \left(x - - 7\right)$

$y - 3 = \frac{5}{2} \left(x + 7\right)$

The slope-intercept for of a linear equation is $\textcolor{red}{y = m x + b}$ where $\textcolor{red}{m}$ is the slope and $\textcolor{red}{b}$ is the y-intercept.

To transform our equation we must solve for $y$ while keeping the equation balanced:

$y - 3 = \frac{5}{2} x + \left(\frac{5}{2} \times 7\right)$

$y - 3 = \frac{5}{2} x + \frac{35}{2}$

$y - 3 + \textcolor{red}{3} = \frac{5}{2} x + \frac{35}{2} + \textcolor{red}{3}$

$y - 0 = \frac{5}{2} x + \frac{35}{2} + \left(3 \times \frac{2}{2}\right)$

$y = \frac{5}{2} x + \frac{35}{2} + \frac{6}{2}$

$y = \frac{5}{2} x + \frac{35 + 6}{2}$

$y = \frac{5}{2} x + \frac{41}{2}$