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
[tex]y = -\frac{7}{2}x - \frac{59}{2}[/tex]
