Question

Write an equation in slope-intercept form for the line that satisfies the following set of conditions.

passes through $\left(3,7\right)\left(-2,-3\right)$.

Short answer

The solution is $y=2x+1$.

Step-by-step solution

Step 1- Consider the set of conditions.

Consider the points $\left(x_1,y_1\right)=\left(3,7\right),\left(x_2,y_2\right)=\left(-2,-3\right)$.

Step 2- Step description.

The slope intercept form is given by the formula $y=mx+b$, where $m$ is the slope.

The slope can be calculated by the formula $m=\frac{y_2-y_1}{x_2-x_1}$.

Step 3- Step description.

Find the slope of the points as follows:

$\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{-3-7}{-2-3}\\ m=\frac{-10}{-5}\\ m=2\end{array}$

Substitute the value of $m$and the set of points $\left(x_1,y_1\right)=\left(3,7\right)$in the slope intercept equation as follows:

$\begin{array}{l}y=mx+b\\ 7=2\left(3\right)+b\\ 7-6=b\\ b=1\end{array}$

Step 4- Step description

Now substitute the value of slope and $b$in the slope intercept form as follows:

$\begin{array}{l}y=mx+b\\ y=2\left(x\right)+1\\ y=2x+1\end{array}$.

Thus, the slope intercept form is$y=2x+1$.