Question

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

Slope 1 passes through (5,3).

Short answer

The solution is $y=x-2$.

Step-by-step solution

Step 1- Consider the set of conditions.

Consider the slope$m=1$ passes through the points $\left(x,y\right)=\left(5,3\right)$.

Step 2- Step description.

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

Step 3- Step description.

Substitute the value of $m$and the set of points in the slope intercept equation as follows:

$\begin{array}{l}y=mx+b\\ 3=1\left(5\right)+b\\ 3=5+b\\ b=3-5\\ b=-2\end{array}$

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

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

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