What is the equation of the line given points (-12,0), (4,4)?

1 Answer
Jul 28, 2018

See a solution process below:

Explanation:

First, we need to determine the slope of the line. The formula for find the slope of a line is:

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

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

Substituting the values from the points in the problem gives:

$m = \frac{\textcolor{red}{4} - \textcolor{b l u e}{0}}{\textcolor{red}{4} - \textcolor{b l u e}{- 12}} = \frac{\textcolor{red}{4} - \textcolor{b l u e}{0}}{\textcolor{red}{4} + \textcolor{b l u e}{12}} = \frac{4}{16} = \frac{1}{4}$

Now, we can use the point-slope formula to write and equation for the line. The point-slope form of a linear equation is: $\left(y - \textcolor{b l u e}{{y}_{1}}\right) = \textcolor{red}{m} \left(x - \textcolor{b l u e}{{x}_{1}}\right)$

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

Substituting the slope we calculated and the values from the first point in the problem gives:

$\left(y - \textcolor{b l u e}{0}\right) = \textcolor{red}{\frac{1}{4}} \left(x - \textcolor{b l u e}{- 12}\right)$

$y = \textcolor{red}{\frac{1}{4}} \left(x + \textcolor{b l u e}{12}\right)$

We can modify this result to put the equation in slope-intercept form. 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.

$y = \textcolor{red}{\frac{1}{4}} \left(x + \textcolor{b l u e}{12}\right)$

$y = \left(\textcolor{red}{\frac{1}{4}} \times x\right) + \left(\textcolor{red}{\frac{1}{4}} \times \textcolor{b l u e}{12}\right)$

y = color(red)(1/4)x + color(blue)(12)/(color(red)(4)

$y = \textcolor{red}{\frac{1}{4}} x + \textcolor{b l u e}{3}$