Question

PLZ HELP...Enter in standard form the equation of the line passing through the given point and having the given slope.

Answer 1

Standard form for the equation of the line is

$y=-\frac{2}{3} x-\frac{25}{3}$

Solution:

Given point is (2, –5).

slope of the line m = $-\frac{2}{3}$

Here, $x_1=2, y_1=-5$

Equation of a line passing through the point:

$y-y_1=m(x-x_1)$

$y-(-5)=-\frac{2}{3} (x-(-5))$

$y+5=-\frac{2}{3} (x+5)$

$y+5=-\frac{2}{3} x-\frac{10}{3}$

Subtract 15 from both sides of the equation.

$y+5-5=-\frac{2}{3} x-\frac{10}{3}-5$

$y=-\frac{2}{3} x-\frac{25}{3}$

Standard form for the equation of the line is

$y=-\frac{2}{3} x-\frac{25}{3}$