Question

Line 1 passes through the points (-5, -8) and (9, -2). Line 2 is perpendicular to Line 1 and passes through the point (3, 18). What is the equation of Line 2?

A) y = -2x + 20
B) y = -2x - 12
C) y = 2x + 12
D) y = 2x - 20

Answer 1

The slope of Line 1 is 3/7. The slope of Line 2, which is perpendicular to Line 1, is -7/3. Using the point (3, 18) to find the y-intercept, the equation of Line 2 is y = (-7/3)x + 25.

Step-by-step explanation:

To find the equation of Line 2, which is perpendicular to Line 1 and passes through the point (3, 18), we first need to determine the slope of Line 1. The slope (∅) is calculated using the formula ∅ = ∅y / ∅x, where ∅y is the change in y and ∅x is the change in x between two points on the line.

For Line 1, using the points (-5, -8) and (9, -2), we calculate:

• ∅y = -2 - (-8) = 6
• ∅x = 9 - (-5) = 14
• ∅ = 6 / 14 = 3 / 7

Since Line 2 is perpendicular to Line 1, its slope will be the negative reciprocal of Line 1's slope. Therefore, the slope of Line 2 is:

• ∅ = -1 / (3 / 7) = -7 / 3

Now we use the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept. With the slope of -7/3 and passing through (3, 18), we can solve for b:

• 18 = (-7/3)(3) + b
• 18 = -7 + b
• b = 18 + 7
• b = 25

So, the equation of Line 2 is y = (-7/3)x + 25.

None of the given options matches this equation, so the student may need to recheck the provided options or the question.