Question

Which of the following is an equation of the line that passes through the point (−2, 3) and is perpendicular to the graph of the equation y = 3x − 2?

Answer 1

The equation of the line is $y=-\frac{1}{3}+\frac{7}{3}$

Explanation:

The given equation is $y=3 x-2$

Slope:

Since, the equation of the line is perpendicular to the equation $y=3 x-2$, then, the slope is given by

$m=-\frac{1}{3}$

Hence, the slope is $m=-\frac{1}{3}$

Equation of the line:

The equation of the line can be determined using the formula,

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

Substituting the point (-2,3) and the slope $m=-\frac{1}{3}$, in the above formula, we get,

$y-3=-\frac{1}{3}(x+2)$

Simplifying, we get,

$y-3=-\frac{1}{3}x-\frac{2}{3}$

     $y=-\frac{1}{3}x-\frac{2}{3}+3$

     $y=-\frac{1}{3}+\frac{7}{3}$

Therefore, the equation of the line is $y=-\frac{1}{3}+\frac{7}{3}$