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?

The equation of the line is

Explanation:

The given equation is

Slope:

Since, the equation of the line is perpendicular to the equation , then, the slope is given by

Hence, the slope is

Equation of the line:

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

Substituting the point (-2,3) and the slope , in the above formula, we get,

Simplifying, we get,

Therefore, the equation of the line is

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.