Write the equation of a line that is perpendicular to y=-2/7x+9 and passes through the point (4,-6)

This is in slope-intercept form, so you can think of it as being y=mx+b. Invert m (the slope) and flip its sign, and then substitute the x and y values in and solve for b. The answer is y=7/2x-20.

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ap8997154 ap8997154 · Answer 2 · 2022-08-05T14:15:51+02:00

The equation of a line that is perpendicular to y=-2/7x+9 and passes through the point (4,-6) is y=(7/2)x-20.

What is the equation of a line?

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,

y =mx + c

where,

x is the coordinate of the x-axis,

y is the coordinate of the y-axis,

m is the slope of the line, and

c is the y-intercept.

The product of the slope of two perpendicular lines is equal to -1. Therefore, the product of the slope can be written as,

(-2/7) × m = -1

(2/7) × m = 1

m = 7/2

Thus, the slope of the perpendicular line is 7/2.

Now, substitute the coordinates of the point and slope in the general equation of the line to get the y-intercept of the line.

y = mx + c

-6 = (7/2)(4) + C

-6 = 14 + C

C = -6 -14

C = -20

Hence, the equation of a line that is perpendicular to y=-2/7x+9 and passes through the point (4,-6) is y=(7/2)x-20.

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