Question

Find the equation of a line with given slope and y-intercept and write the equation in slope-intercept form.

Slope$\frac{-3}{4}$and y-intercept$\left(0,-2\right)$.

Short answer

Slope intercept form of the line is$y=\frac{-3}{4}x-2$.

Step-by-step solution

Step 1. Given information.

Slope of a line is$\frac{-3}{4}$and y-intercept is$\left(0,-2\right)$.

Step 2. Identify the slope and points.

Slope is$\frac{-3}{4}$and point$\left(x_1,y_1\right)=\left(0,-2\right)$.

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

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

Now, substitute the values.

localid="1644384521540" $\begin{array}{rcl}y-\left(-2\right)& =& \frac{-3}{4}\left(x-0\right)\\ y+2& =& \frac{-3}{4}x\end{array}$

Step 4. Write the slope-intercept form.

Equation of the line in slope-intercept form is$y=\frac{-3}{4}x-2$.