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Write the equation of the line perpendicular to y=5/4x+3/4 that passes through the point (-4,9)

User Estevez
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Answer:

Therefore, the equation of the line perpendicular to y = 5/4x + 3/4 that passes through the point (-4, 9) is y = (-4/5)x + 23/5.

Explanation:

To find the equation of the line perpendicular to y = 5/4x + 3/4, we need to determine its slope. We know that the slope of a line perpendicular to this line will be the negative reciprocal of its slope.

The slope of y = 5/4x + 3/4 is 5/4, so the slope of the perpendicular line will be -4/5.

Now we can use the point-slope form of the equation of a line to find the equation of the perpendicular line that passes through the point (-4, 9):

y - y1 = m(x - x1)

Where m is the slope of the line and (x1, y1) is the given point.

Substituting in m = -4/5 and (x1, y1) = (-4, 9), we get:

y - 9 = (-4/5)(x + 4)

Expanding and simplifying, we get:

y = (-4/5)x + 23/5

Therefore, the equation of the line perpendicular to y = 5/4x + 3/4 that passes through the point (-4, 9) is y = (-4/5)x + 23/5.

User Hnin
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