Question

Find the equation of the line that satisfies the given conditions.(Lesson 1.10)

Through$\left(-3,-5\right)$; slope:$-\frac{7}{2}$

Short answer

Equation of the line is $7x+2y+31=0$.

Step-by-step solution

Step 1. Definition of point-slope form.

Point-slope form is the equation of a straight line in the form $y-y_1=m\left(x-x_1\right)$, where m is the slope of the line and$\left(x_1,y_1\right)$ are the coordinates of the given point on the line.

Step 2. Plug the value in equation in general form.

Use the point-slope form to write the equation of the line with $x_1=-3$, $y_1=-5$, and the slope is $m=-\frac{7}{2}$

$\begin{array}{l}y-y_1=m\left(x-x_1\right)\\ y-5=-\frac{7}{2}\left(x-\left(-3\right)\right)\end{array}$

Step 3. Calculate the equation of the line in standard form.

$\begin{array}{l}y+5=-\frac{7}{2}\left(x+3\right)\\ 2\left(y-5\right)=-7\left(x+3\right)\\ 2y+10=-7x-21\\ 2y+10+7x+21=0\\ 7x+2y+31=0\end{array}$