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saveliy_v [14]
3 years ago
9

Which of the following is the equation of the line that is perpendicular to y=-4x-5 and goes through the point (-2, 3)? Question

14 options: y=-4x-5 y=-1/4x+5/2 y=1/4x+7/2 y=4x+11
Mathematics
1 answer:
Scrat [10]3 years ago
8 0

Answer:

The equation of the perpendicular line to y=-4*x-5 is y=\frac{1}{4}*x+\frac{7}{2}

Step-by-step explanation:

Perpendicular lines are two or more lines that intersect at an angle of 90 degrees. Being  y = m * x + b the equation of a line, two lines, with a slope other than zero, are orthogonal or perpenducillary if and only if the product of their slopes is -1. In other words, if two lines are perpendicular, they have their slopes reversed and sign changed.

In this case, with y = -4x-5 the slope will be -4. So the slope of the perpendicular line will be \frac{1}{4}. Then the equation of the perpendicular line will be:

y=\frac{1}{4}* x+b

To find the value of b, you know the value of the point (-2,3). So x = -2 and y = 3. Replacing in the equation of the perpendicular line, you have:

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

Solving, you get:

3=-\frac{1}{2}+b

3+\frac{1}{2}=b

\frac{7}{2}=b

<u><em>The equation of the perpendicular line to y=-4*x-5 is </em></u>y=\frac{1}{4}*x+\frac{7}{2}<u><em></em></u>

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Step-by-step explanation:

−4(4−x)=4/5(x+16)

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