83.6k views
2 votes
Write the equation of a line perpendicular to the one above that passes through (-2, 9). You may use either slope intercept or point slope form.

Write the equation of a line perpendicular to the one above that passes through (-2, 9). You-example-1
User Ghan
by
8.1k points

1 Answer

2 votes

Answer:

-3x + 3

Explanation:

To find the equation of a line perpendicular to the line passing through (-2, 1) and (4, 3), we need to determine the slope of the original line first. Then, we can use the negative reciprocal of that slope to find the slope of the perpendicular line. Finally, we can use the point-slope form to write the equation of the perpendicular line.

Step 1: Find the slope of the original line.

Slope (m) = (change in y) / (change in x)

m = (3 - 1) / (4 - (-2))

m = 2 / 6

m = 1/3

Step 2: Determine the slope of the perpendicular line.

The slope of the perpendicular line is the negative reciprocal of the original line's slope.

Perpendicular slope = -1 / (1/3)

Perpendicular slope = -3

Step 3: Use the point-slope form to write the equation.

The point-slope form is given by:

y - y1 = m(x - x1)

Using the point (-2, 9) and the perpendicular slope (-3), we can write the equation as:

y - 9 = -3(x - (-2))

y - 9 = -3(x + 2)

y - 9 = -3x - 6

y = -3x + 3

Therefore, the equation of the line perpendicular to the line passing through (-2, 1) and (4, 3) and passing through (-2, 9) is y = -3x + 3.

User Vimdude
by
7.6k points

No related questions found