Question

Find the slope of a line perpendicular to each given line.
Y = -1/2x - 2

y + 7 = 5/2(4x + 6)
could you show the steps

Answer 1

To find the slope of a line perpendicular to the given line, we need to determine the slope of the given line first. The given line is in the form y = mx + b, where m represents the slope.

For the first line, y = (-1/2)x - 2, the slope is -1/2.

For the second line, y + 7 = (5/2)(4x + 6), we need to rewrite it in slope-intercept form. Let's distribute the (5/2) on the right side of the equation:

y + 7 = (5/2)(4x) + (5/2)(6)
y + 7 = 10x + 15

Subtract 7 from both sides to isolate y:

y = 10x + 15 - 7
y = 10x + 8

Now the second line is in the form y = mx + b, where m represents the slope. The slope of this line is 10.

To find the slope of a line perpendicular to a given line, we take the negative reciprocal of the slope.

For the first line, the negative reciprocal of -1/2 is 2.

For the second line, the negative reciprocal of 10 is -1/10.