How do you write an equation of a line with points (-1,3), (0,8)?

Jun 3, 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:

$m = \frac{\textcolor{red}{8} - \textcolor{b l u e}{3}}{\textcolor{red}{0} - \textcolor{b l u e}{- 1}} = \frac{\textcolor{red}{8} - \textcolor{b l u e}{3}}{\textcolor{red}{0} + \textcolor{b l u e}{1}} = \frac{5}{1} = 5$

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 above and the values from the first point in the problem gives:

$\left(y - \textcolor{b l u e}{3}\right) = \textcolor{red}{5} \left(x - \textcolor{b l u e}{- 1}\right)$

$\left(y - \textcolor{b l u e}{3}\right) = \textcolor{red}{5} \left(x + \textcolor{b l u e}{1}\right)$

We can also substitute the slope we calculated above and the values from the second point in the problem giving:

$\left(y - \textcolor{b l u e}{8}\right) = \textcolor{red}{5} \left(x - \textcolor{b l u e}{0}\right)$

$\left(y - \textcolor{b l u e}{8}\right) = \textcolor{red}{5} x$

We can also convert this equation to slope-intercept form:

$y - \textcolor{b l u e}{8} = \textcolor{red}{5} x$

$y - \textcolor{b l u e}{8} + 8 = \textcolor{red}{5} x + 8$

$y - 0 = 5 x + 8$

$y = 5 x + 8$

Jun 3, 2018

$y = 5 x + 8$

Explanation:

$\text{the equation of a line in "color(blue)"slope-intercept form}$ is.

•color(white)(x)y=mx+b

$\text{where m is the slope and b the y-intercept}$

$\text{to calculate m use the "color(blue)"gradient formula}$

•color(white)(x)m=(y_2-y_1)/(x_2-x_1)

$\text{let "(x_1,y_1)=(-1,3)" and } \left({x}_{2} , {y}_{2}\right) = \left(0 , 8\right)$

$m = \frac{8 - 3}{0 - \left(- 1\right)} = \frac{5}{1} = 5$

$\text{note that "b=8" since point } \left(0 , 8\right)$

$y = 5 x + 8 \leftarrow \textcolor{red}{\text{is equation of line}}$