Question

Enter an equation of the line (in slope-intercept form) that passes through the point (20, −7) and is perpendicular to the line y = −5x + 9. Express any numeric values as integers or simplified fractions.

Answer 1

y = 1/5x -11

Explanation:

You want the slope-intercept equation of the line perpendicular to y=-5x+9 that goes through the point (20, -7).

Slope-intercept form

The slope-intercept form of the equation for a line is ...

y = mx +b . . . . . . . . where m is the slope and b is the y-intercept

This can be solved to find the y-intercept from a point on the line:

b = y -mx

Comparing this form to the given equation, you see the given line has a slope of m = -5.

Perpendicular line

The perpendicular line will have a slope that is the opposite reciprocal of the slope of the given line:

slope = -1/(-5) = 1/5

Y-intercept

The y-intercept of the desired line can be found using the equation for b above. The y-intercept of the line with slope 1/5 through point (x, y) = (20, -7) is ...

b = y -mx = (-7) -1/5(20) = -7 -4

b = -11

Now, we have the slope and intercept of the desired line, so we can write its equation:

y = 1/5x -11