Question

Write the equation of the line perpendicular to y = x+ 5 that passes through the point ( -7,3).

Type an equation using slope-intercept form or using the given point in point-slope form.

Answer 1

y = - x - 4

Explanation:

A line perpendicular to the line: y = x + 5

must have a slope that is the "opposite of the reciprocal" of the slope of the given line. Then the slope of the perpendicular line must be "-1".

Now that we know the slope of the perpendicular line, we use the point (-7, 3) to complete the equation of the line:

y = -1 x + b

3 = -1 (-7) + b

then we solve for "b":

3 = 7 + b

3 - 7 = b

b = -4

Now we can write the total equation of the perpendicular line in slope-intercept form as:

y = - x - 4