Q68. - Algebra 2

Question

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

 

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

Step-by-Step Solution

Answer

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

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 $y=2x+1$.