Question

Identify an equation in point-slope form for the line perpendicular to y = –2x + 8 that passes through (–3, 9).

1) y = 2x + 15
2) y = -2x - 15
3) y = -2x + 15
4) y = 2x - 15

Answer 1

The equation in point-slope form for the line perpendicular to y = -2x + 8 that passes through (-3, 9) is y = 1/2x + 15/2.

Step-by-step explanation:

To find the equation of the line perpendicular to y = -2x + 8 and passing through the point (-3, 9), we need to determine the slope of the perpendicular line. The slope of the original line is -2, so the slope of the perpendicular line would be the negative reciprocal, which is 1/2. Using the point-slope form equation y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope, we can plug in the values to get y - 9 = 1/2(x - (-3)). Simplifying the equation gives us y - 9 = 1/2(x + 3), which can be rearranged as y = 1/2x + 15/2. Therefore, the equation in point-slope form for the line perpendicular to y = -2x + 8 that passes through (-3, 9) is y = 1/2x + 15/2.