Question

Use slopes to determine if the lines 5x−4y=−1 and 4x−y=−9 are perpendicular.

Answer 1

The lines are not perpendicular.

Explanation:

If the lines are perpendicular, the product of the slopes should be -1.

These equations are in standard form (Ax + By = C), so we can easily find the slopes through using equation: slope= - A / B

For line 5x−4y=−1,

slope = -A / B

= - 5 /- 4

= 5/4

For line 4x−y=−9

slope = -A / B

= - 4 / -1

= 4

Now multiply the slopes to find the product:

5 /4 x 4

= 5

Since 5 ≠ -1, the lines are not perpendicular.

Answer 2

Not perpendicular

Explanation:

Convert it to y-intercept form first:

5x - 4y = -1

-4y = -5x - 1

y = 5/4x + 1/4

4x - y = -9

-y = -4x - 9

y = 4x + 9

y = 5/4x + 1/4

y = 4x + 9

From the slopes, they are not considered perpendicular because one of the line slope is not a negative reciprocal of the other line slope.