Question

A line is perpendicular to y = x - 8

and intersects the point (2, 2).
What is the equation of this
perpendicular line?
y = [?]x + []
Hint: Use the Point-Slope Form: y - y₁ = m(x-x₁)
Then write the equation in slope-intercept form.
Enter

Answer 1

To find the equation of the line that is perpendicular to y = x - 8 and intersects the point (2, 2), we can use the point-slope form of a line:

y - y₁ = m(x-x₁)

Where (x₁, y₁) is the point of intersection, and m is the slope of the line.

We know that the slope of a line perpendicular to y = x - 8 is the negative reciprocal of the slope of y = x - 8. The slope of y = x - 8 is 1, so the slope of the perpendicular line is -1.

We also know that the line intersects the point (2, 2), so we can plug these values into the point-slope form to get:

y - 2 = -1(x-2)

We can then simplify this equation to get:

y - 2 = -x + 2

y = -x + 4

This is the equation of the line that is perpendicular to y = x - 8 and intersects the point (2, 2).