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2 answers:
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Slope-intercept form:
y = mx + b "m" is the slope, "b" is the y-intercept (the y value when x = 0)
First find the slope of the line that passes through (4,9) and (-3,6).
Use the slope formula and plug in the two points:
A.) For lines to be parallel, their slopes have to be the same.
Since the given line's slope is 3/7, the parallel line's slope is also 3/7
y = 3/7x + b To find "b", plug in the point (14,8) into the equation
8 = 3/7(14) + b
8 = 42/7 + b
8 = 6 + b Subtract 6 on both sides
2 = b
B.) For lines to be perpendicular, their slopes have to be the opposite/negative reciprocal (flipped sign and number)
For example:
slope is 3
perpendicular line's slope is -1/3
slope is -2/3
perpendicular line's slope is 3/2
Since the given line's slope is 3/7, the perpendicular line's slope is -7/3
y = -7/3x + b Plug in (14, 8) to find "b"
8 = -7/3(14) + b
8 = -98/3 + b Add 98/3 on both sides
8 + 98/3 = b Make the denominators the same
24/3 + 98/3 = b
122/3 = b