# What is the slope intercept form of the line passing through (15,3)  with a slope of 1/2 ?

Jun 18, 2018

See a solution process below:

#### Explanation:

The slope-intercept form of a linear equation is: $y = \textcolor{red}{m} x + \textcolor{b l u e}{b}$

Where $\textcolor{red}{m}$ is the slope and $\textcolor{b l u e}{b}$ is the y-intercept value.

First, we can substitute the slope in the problem for $\textcolor{red}{m}$ and substitute the values from the point in the problem for $x$ and $y$ and solve for $\textcolor{b l u e}{b}$:

$3 = \left(\textcolor{red}{\frac{1}{2}} \times 15\right) + \textcolor{b l u e}{b}$

$3 = \textcolor{red}{\frac{15}{2}} + \textcolor{b l u e}{b}$

$3 - \frac{15}{2} = \textcolor{red}{\frac{15}{2}} - \frac{15}{2} + \textcolor{b l u e}{b}$

$\left(\frac{2}{2} \times 3\right) - \frac{15}{2} = 0 + \textcolor{b l u e}{b}$

$\frac{6}{2} - \frac{15}{2} = \textcolor{b l u e}{b}$

$\frac{6 - 15}{2} = \textcolor{b l u e}{b}$

$- \frac{9}{2} = \textcolor{b l u e}{b}$

$\textcolor{b l u e}{b} = - \frac{9}{2}$

We can now substitute $- \frac{9}{2}$ for $\textcolor{b l u e}{b}$ and the slope from the problem for $\textcolor{red}{m}$ in the original formula to write the equation:

$y = \textcolor{red}{\frac{1}{2}} x + \textcolor{b l u e}{- \frac{9}{2}}$

$y = \textcolor{red}{\frac{1}{2}} x - \textcolor{b l u e}{\frac{9}{2}}$