Question 246219
Write an equation in slope-intercept form for the line that passes through the point (-4,6) and is perpendicular to y=8x-7.

The slope intercept form of a line is y = mx+b where m is the slope of the line and b is the value of y when the line crosses the y-axis (or when x = 0).

The line y = 8x-7 is in slope-intercept form so its slope is 8. The line perpendicular to this line has a slope that is the negative reciprical of 8 which is -1/8.

So the new line has the equation y = -1/8x + b

Since the new line passes through (-4,6) we can substitute x=-4 and y=6 in the equation above so:

6 = (-1/8)*-4 + b
6 = 1/2 + b
b = 5.5
The equation of the perpendicular line has the equation  y = -1/8x + 5.5