# How do you write an equation in slope-intercept form of the line that passes through the points (3,0.5) and (10, -0.2)?

Mar 28, 2017

See the entire solution process below:

#### Explanation:

First we must determine the slope of the line. The slope can be found by using the formula: $m = \frac{\textcolor{red}{{y}_{2}} - \textcolor{b l u e}{{y}_{1}}}{\textcolor{red}{{x}_{2}} - \textcolor{b l u e}{{x}_{1}}}$

Where $m$ is the slope and ($\textcolor{b l u e}{{x}_{1} , {y}_{1}}$) and ($\textcolor{red}{{x}_{2} , {y}_{2}}$) are the two points on the line.

Substituting the values from the points in the problem gives:

$m = \frac{\textcolor{red}{- 0.2} - \textcolor{b l u e}{0.5}}{\textcolor{red}{10} - \textcolor{b l u e}{3}} = - \frac{0.7}{7} = - \frac{7}{70} = - \frac{1}{10} = - 0.1$

Next, we can write an equation for the line using the point-slope formula. The point-slope formula states: $\left(y - \textcolor{red}{{y}_{1}}\right) = \textcolor{b l u e}{m} \left(x - \textcolor{red}{{x}_{1}}\right)$

Where $\textcolor{b l u e}{m}$ is the slope and $\textcolor{red}{\left(\left({x}_{1} , {y}_{1}\right)\right)}$ is a point the line passes through.

Substituting the slope we calculated and the first point from the problem we can write:

$\left(y - \textcolor{red}{0.5}\right) = \textcolor{b l u e}{- 0.1} \left(x - \textcolor{red}{3}\right)$

To put this into slope-intercept form we can solve for $y$. 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.

$y - \textcolor{red}{0.5} = \textcolor{b l u e}{- 0.1} \left(x - \textcolor{red}{3}\right)$

$y - \textcolor{red}{0.5} = \left(\textcolor{b l u e}{- 0.1} \times x\right) - \left(\textcolor{b l u e}{- 0.1} \times \textcolor{red}{3}\right)$

$y - \textcolor{red}{0.5} = - 0.1 x + 0.3$

$y - \textcolor{red}{0.5} + 0.5 = - 0.1 x + 0.3 + 0.5$

$y - 0 = - 0.1 x + 0.8$

$y = \textcolor{red}{- 0.1} x + \textcolor{b l u e}{0.8}$