Question

Write an equation in slope-intercept form of the line with slope $-\frac{2}{3}$ that passes through $(-2,5)$.

Short answer

The equation of line in slope intercept form is $2x+3y=11$

Step-by-step solution

Step-1 –Determining the Slope and Point

The slope of the equation, $m=-\frac{2}{3}$

The point passes through line is $(-2,5)$

Step-2-General equation of Slope Intercept form

$y-{}_{}{y}_1=m(x-x_1)$

Where $x_1$and $y_1$are a point the line intersects and $m$is the slope.

Step-3 –Determining the Equation in slope intercept form

$m=-\frac{2}{3}$, $x_1=-2$, $y_1=5$

localid="1647534724888" $\begin{array}{c}y-y_1=m(x-x_1)\\ or,y-5=-\frac{2}{3}(x+2)\\ or,y-5=-\frac{2}{3}x-\frac{4}{3}\\ or,3y-15=-2x-4\\ or,2x+3y=11\end{array}$