Question

Write an equation in slope-intercept form that satisfies each set of conditions.

32. Passes through $\left(5,-3\right) and \left(-2,0\right)$

Short answer

The equation of line is $y=-\frac{3}{7}x-\frac{6}{7}$.

Step-by-step solution

Step-1 – Slope of a line and point slope form.

The slope of the line is $slope=\frac{y_2-y_1}{x_2-x_1}$

The point slope form is $y-y_1=m(x-x_1)$ where m is the slope of the line.

Step-2 – Calculate the slope.

Substitute $(x_1,y_1)=(5,-3) and (x_2,y_2)=(-2,0)$into the formula $slope=\frac{y_2-y_1}{x_2-x_1}$

$\begin{array}{l}m=\frac{0-(-3)}{-2-5}\\ m=\frac{3}{-7}\\ m=-\frac{3}{7}\end{array}$

Step-3 – Make the equation.

Substitute $(x_1,y_1)=(5,-3) and m=-\frac{3}{7}$into $y-y_1=m(x-x_1)$.

$\begin{array}{l}y-(-3)=-\frac{3}{7}(x-5)\\ y+3=-\frac{3}{7}x+\frac{15}{7}\\ y=-\frac{3}{7}x-\frac{6}{7}\end{array}$

The equation of line is $y=-\frac{3}{7}x-\frac{6}{7}$.