Question

Find the equation of the line through (-7, -2) that is perpendicular to the line y = x/3+6.

Answer 1

Answer:

y = −3x − 23

Step-by-step explanation:

The equation of the line in the slope-intercept form is y= x/3 + 6.

The slope of the perpendicular line is negative inverse: m = −3.

So, the equation of the perpendicular line is y = −3x + a.

To find a, we use the fact that the line should pass through the given point:

−2 = (−3) ⋅ (−7) + a.

Thus, a = −23.

Therefore, the equation of the line is y = −3x − 23.

Answer: y =−3x − 23