Q. 47 - Precalculus Enhanced with Graphing Utilities

Question

Find an equation for the line with the given properties. Express your answer using either the general form or the slope–intercept form of the equation of a line, whichever you prefer.

Slope $-\frac{2}{3}$, containing the point $(1,-1)$

Step-by-Step Solution

Answer

The equation of line is $2x+3y=-1$

Step 1. Given Information

The given slope of line is $-\frac{2}{3}$ and containing the point $(1,-1)$

Step 2. Calculation

Substitute the given values in the general form of point slope equation of line.

$$\begin{gathered} y-y_1=m(x-x_1) \\ y-(-1)=(-\frac{2}{3})(x-1) \\ y+1=-\frac{2}{3}x+\frac{2}{3} \\ 3y+3=-2x+2 \\ 3y=-2x-1 \\ 2x+3y=-1 \end{gathered}$$