How do you find the equation in slope - intercept form, of the line passing through the points (-1, 2) and (3, -4)?

1 Answer
Jul 19, 2017

See a solution process below:

Explanation:

First, we need to determine the slope of the line for the equation. 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:

$m = \frac{\textcolor{red}{- 4} - \textcolor{b l u e}{2}}{\textcolor{red}{3} - \textcolor{b l u e}{- 1}} = \frac{\textcolor{red}{- 4} - \textcolor{b l u e}{2}}{\textcolor{red}{3} + \textcolor{b l u e}{1}} = - \frac{6}{4} = - \frac{3}{2}$

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.

Because we have calculated the slope and the problem gives us a point from the line, we can substitute the slope we calculated for $m$ and we can substitute the values from either of the points in the problem and solve for $b$:

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

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

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

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

$- \textcolor{red}{\frac{3}{2}} + \frac{4}{2} = \textcolor{b l u e}{b}$

$\frac{1}{2} = \textcolor{b l u e}{b}$

We can now substitute the slope and $b$ value we calculated into the formula to give the equation in slope-intercept form:

$y = \textcolor{red}{- \frac{3}{2}} x + \textcolor{b l u e}{\frac{1}{2}}$