Question

Write the slope-intercept form of the equation of the line that is perpendicular to AB and passes through

Point X. Show all work for full credit.
A
(-10, 8)
-10
-8
X
(-5, 10)
-6
-4 -2
YA
10
8
4
2 B
-2
4
6
-8
-10
(2, 3)
2
4
6 8 10
X
A

Answer 1

To find the slope of line AB, we use the slope formula:

slope of AB = (yB - yA) / (xB - xA)

where A = (-10, 8) and B = (2, 3).

slope of AB = (3 - 8) / (2 - (-10)) = -5/12

The slope of a line perpendicular to AB will have a negative reciprocal slope, so its slope will be 12/5.

Using the slope-intercept form of the equation of a line:

y = mx + b

where m is the slope and b is the y-intercept, we can find the equation of the line that passes through point X (-5, 10) and has a slope of 12/5.

10 = (12/5)(-5) + b

10 = -24/5 + b

b = 74/5

Therefore, the equation of the line that is perpendicular to AB and passes through point X is:

y = (12/5)x + 74/5