find an equation of the line that satisfies the given conditions

Question

Find an equation of the line that satisfies the given conditions.

Through (−9, −12);  perpendicular to the line passing through (−6, 0) and (−2, −2)

Answer 1

Whenever you see a coordinate geometry problem involving perpendicular lines, you should think that their slopes must be negative reciprocals. Therefore, let's find the slope of the second line. Use the formula slope = rise/run to get slope = -1/2. That means that the slope of the first line must be 2. Because we have a point on the line and its slope, we can use the point-slope formula:

y = m(x - x₀) + y₀

y = 2(x - -9) - 12

y = 2(x + 9) - 12

(You can distribute the 2 and combine like terms if you want to get that in slope-intercept form.)