Which equation is the equation of a line that passes through (–10, 3) and is perpendicular to y = 5x – 7? (1 point) Responses y = 5x + 53 y = 5 x + 53 y = –x%C2%A0– 7 y = – Image with alt text: one-fifth x %C2%A0– 7 y = –x%C2%A0+ 1 y = – Image with alt text: one-fifth x %C2%A0+ 1 y = x + 5
The equation of a line that is perpendicular to y = 5x – 7 will have a slope that is the negative reciprocal of the slope of y = 5x – 7. The slope of y = 5x – 7 is 5, so the slope of the perpendicular line will be -1/5.
Using the point-slope form of the equation of a line, y - y1 = m(x - x1), where (x1, y1) are the coordinates of a point on the line and m is the slope, we can substitute the values (-10, 3) and -1/5:
y - 3 = -1/5(x - (-10))
y - 3 = -1/5(x + 10)
y - 3 = -1/5x - 2
y = -1/5x + 1
Therefore, the equation of the line that passes through (-10, 3) and is perpendicular to y = 5x – 7 is y = -1/5x + 1.