Consider the line y=2/7x+5 find the equation of the line that is parallel and perpendicular to this line and passes through the point(-7,-5)

Slope-intercept form is:

y = mx + b

"m" is the slope, "b" is the y-intercept (the y value when x = 0)

You need to find "m" and "b"

PARALLEL:

For lines to be parallel, they have to have the SAME slope. The given line's slope is 2/7, so the parallel line's slope is also 2/7

y = 2/7x + b

To find "b", you can plug in the point (-7, -5) into the equation

y = 2/7x + b

-5 = 2/7(-7) + b

-5 = -2 + b      Add 2 on both sides

-3 = b

y = 2/7x - 3

PERPENDICULAR:

For lines to be perpendicular, their slopes have to be the opposite/negative reciprocal (flipped sign and number)

For example:

slope is 2

perpendicular line's slope is -1/2

slope is -2/5

perpendicular line's slope is 5/2

The given line's slope is 2/7, so the perpendicular line's slope is -7/2.

y = -7/2x + b

To find "b", plug in (-7,-5) into the equation

y = -7/2x + b

-5 = -7/2(-7) + b

-5 = 49/2 + b       Subtract 49/2 on both sides

-5 - 49/2 = b      Make the denominators the same

-10/2 - 49/2 = b

-59/2 = b

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step-by-step explanation:

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