Question

Find the equation of a line with a given slope andy-intercept and Write the equation in slope-intercept form.

slope $\frac{1}{5}$and y-intercept $\left(0,-5\right)$.

Short answer

Equation of the line in slope Intercept form is $y=\frac{1}{5}x-5$.

Step-by-step solution

Step 1. Given information.

Slope $\frac{1}{5}$ and y-intercept $\left(0,-5\right)$.

Slope intercept form is $y=mx+c$where m is the slope and c the y-intercept.

Step 2. Identify the slope and point.

Slope is$\frac{1}{5}$and point$\left(x_1,y_1\right)=\left(0,-5\right)$.

Step 3. Substitute the values in the point-slope form.

Point-slope form is $y-y_1=m\left(x-x_1\right)$.

Now, substitute the values.

localid="1644383612752" $\begin{array}{rcl}y-\left(-5\right)& =& \frac{1}{5}\left(x-0\right)\\ y+5& =& \frac{1}{5}x\end{array}$

Step 4. Write the equation in slope-intercept form.

Equation of the line with slope $\frac{1}{5}$ and y-intercept $\left(0,-5\right)$is $y=\frac{1}{5}x-5$.