Question

passes through (5,-2) perpendicular to -8x + 9y =-22.

Answer 1

The point is (5, - 2) and the line is - 8x + 9y = - 22

Write the equation in slope - intercept form y = mx + b, where m is slope and b is y - intercept.

- 8x + 9y = - 22

Add 8x to each side.

9y = - 22 + 8x

Divide each side by 9.

y = (8/9)x + (- 22/9).

Compare the above equation with slope - intercept form y = mx + b.

Slope (m) = 8/9.

So,perpendecular line slope is (- 1/m) - 9/8.

Line equation : y - y₁ = (- 1/m)(x -x₁)

y + 2 = (- 9/8)(x - 5)

Subtract 2 from each side.

y = (- 9/8)(x - 5) - 2

y = (- 9/8)x + (45/8) - 2

y = (- 9/8)x + (29/8).

The perpendecular line equation is y = (- 9/8)x + (29/8).

Answer 2

The point is and the equation of line is .

Rewrite the equation in the slope - intercept form: where m is slope and b is y - intercept.

Add 8x to each side.

Divide each side by 9.

.

Therefore slope of given line is .

Because the slopes of perpendicular lines are negative reciprocals, the slope of perpendicular line through is .

To find the y - intercept of perpendicular line, substitute the values of

in the slope - intercept from: and solve for b.

.

Substitute the values of in the slope - intercept form of equation .

 

The equation of perpendicular line is .