Question

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

Passes through $\left(0,5\right)\left(10,10\right)$.

Short answer

The solution is $y=\frac{1}{2}x+5$.

Step-by-step solution

Step 1- Consider the set of conditions.

Consider the points $\left(x_1,y_1\right)=\left(0,5\right),\left(x_2,y_2\right)=\left(10,10\right)$.

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:

$\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{10-5}{10-0}\\ m=\frac{5}{10}\\ m=\frac{1}{2}\end{array}$

Substitute the value of $m$and the set of points $\left(x_1,y_1\right)=\left(0,5\right)$in the slope intercept equation as follows:

$\begin{array}{l}y=mx+b\\ 5=0\left(\frac{1}{2}\right)+b\\ b=5\end{array}$.

Step 4- Step description

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

$\begin{array}{l}y=mx+b\\ y=\frac{1}{2}\left(x\right)+5\\ y=\frac{1}{2}x+5\end{array}$.

Thus, the slope intercept form is$y=\frac{1}{2}x+5$.