18. Write an equation in point-slope form for the line that is perpendicular to the given line and passes through the given point. Show your work.
y−3=4(x+2) through the point (−2, 6)
First, let's find the slope of the given line. The equation is already in the point-slope form, which is y - y1 = m(x - x1).
The slope of the line is the coefficient of x, which is 4.
A line that is perpendicular to another line has a slope that is the negative reciprocal of the slope of the given line. Therefore, the slope of the perpendicular line is -1/4.
Now, we can use the point-slope form with the given point (−2, 6).
y - y1 = m(x - x1)
y - 6 = -1/4 (x - (-2))
y - 6 = -1/4 (x + 2)
y - 6 = -1/4x - 1/2
y = -1/4x - 1/2 + 6
y = -1/4x + 11/2
Therefore, the equation of the line that is perpendicular to y−3=4(x+2) and passes through the point (−2, 6) is y = -1/4x + 11/2.