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sveticcg [70]
3 years ago
15

find the equation of the line passing through the given point and perpendicular to the given equation write your answer in slope

intercept form

Mathematics
1 answer:
Paraphin [41]3 years ago
5 0

Slope-intercept form:

y = mx + b      "m" is the slope, "b" is the y-intercept


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

For example:

slope is 2

perpendicular line's slope is -1/2

slope is -2/3

perpendicular line's slope is 3/2



3.) y = 2x - 2

The given line's slope is 2, so the perpendicular line's slope is -1/2

y=-\frac{1}{2}x+b To find "b", plug in the point (-5 , 5) into the equation

5=-\frac{1}{2}(-5)+b

5=\frac{5}{2}+b     Subtract 5/2 on both sides

5-\frac{5}{2}=b   Make the denominators the same

\frac{10}{2}-\frac{5}{2}=b

\frac{5}{2}=b


y=-\frac{1}{2}x+\frac{5}{2}



4.) -6x + 5y = -10     Get "y" by itself, add 6x on both sides

5y = -10 + 6x          Divide 5 on both sides

y=-2+\frac{6}{5}x

The given line's slope is 6/5, so the perpendicular line's slope is -5/6.

y=-\frac{5}{6}x+b       Plug in (-2, 5)

5 = -\frac{5}{6}(-2)+b

5=\frac{10}{6}+b\\ 5=\frac{5}{3}+b    Subtract 5/3 on both sides

5-\frac{5}{3} =b    Make the denominators the same

\frac{15}{3}-\frac{5}{3}=b\\\frac{10}{3} =b


y = -\frac{5}{6}x+\frac{10}{3}



7.) Perpendicular line's slope is -2

y = -2x + b      Plug in (1,4)

4 = -2(1) + b

4 = -2 + b

6 = b


y = -2x + 6



8.) Perpendicular line's slope is -1/4

y = -\frac{1}{4}x+b     Plug in (-5 , 2)

2=-\frac{1}{4}(-5)+b

2 = \frac{5}{4}+b    Subtract 5/4 on both sides

2-\frac{5}{4}=b     Make the denominators the same

\frac{8}{4}-\frac{5}{4}=b

\frac{3}{4}=b


y=-\frac{1}{4}x+\frac{3}{4}

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