1. write an equation of a line perpendicular to line ab below in slope-intercept form that passes through the point (7, 6).
line ab is shown. a is at 0, 1. b is at negative 2, 5.
y = 0.5x + 2.5
y = 0.5x − 2.5
y = −2x + 20
y = 2x − 20
2. write an equation of a line perpendicular to y = 1 over 4x + 4 in slope-intercept form that passes through the point (−2, 6).
y= 1/4x − 4
y= 1/4x + 6
y= −4x − 2
y= −4x + 1/4

A.

B.

Step-by-step explanation:

A. Find the equation for the line that passes trough AB:

Use the point-slope form to get the slope-intercept form:

The perpendicular line will have and slope that is the negative reciprocal of (that means )

Using the point (7,6)

B. The slope in is , then is:

Using the point (−2, 6)

Parallel lines and their slopes are easy. Since slope is a measure of the angle of a line from the horizontal, and since parallel lines must have the same angle, then parallel lines have the same slope — and lines with the same slope are parallel.

Perpendicular lines are a bit more complicated. If you visualize a line with positive slope (so it's an increasing line), then the perpendicular line must have negative slope (because it will be a decreasing line). So perpendicular slopes have opposite signs. The other "opposite" thing with perpendicular slopes is that their values are reciprocals; that is, you take the one slope value, and flip it upside down. Put this together with the sign change, and you get that the slope of the perpendicular line is the "negative reciprocal" of the slope of the original line — and two lines with slopes that are negative reciprocals of each other are perpendicular to each other. In numbers, if the one line's slope is m = 4/5, then the perpendicular line's slope will be m = –5/4. If the one line's slope is m = –2, then the perpendicular line's slope will be m =1/2.

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step-by-step explanation:

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step-by-step explanation: