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Write the​ slope-intercept equation of the function f whose graph satisfies the given conditions. graph of f passes through (-8,8) and is perpendicular to the line that has an x-intercept of 4 and a y-intercept of -8. what is the equation of the line?

User Jberg
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Answer:

f(x) = -(1/2)x + 4

Explanation:

Let's look for an equation for a straight line of the form y=mx+b, where m is the slope and b is the y-intercept.

We are told this line is perpendicular to a line that has two points identified: (4,0) and (0,-8).

To start, we need to determine the slope of the second line, Slope is the Rise/Run of a line. We can calculate both from the two points given:

(0,-8) to (4,0)

Rise (change in y) = (0-(-8)) = 8

Run = change in x = (4 - 0) = 4

Slope = Rise/Run = (8/4) or 2

The reference line has a slope of 2. Any line that is perpendicular to this line will have a slope that is the negative inverse of the reference line:

negative inverse of slope 2 is slope -(1/2)

The new line has a slope of -(1/2).

We can write y = -(1/2)x + b

Any value of b will still produce a perpendicular line to the reference line. But we are told the new line goes through point (-8,8). To find a value of b that moves the line to go though (-8,8), just enter these coordinates into the equation above and solve for b:

y = -(1/2)x + b

8 = -(1/2)(-8) + b for (-8,8)

8 = -(1/2)(-8) + b

8 = 4 + b

b = 4

The equation becomes y = -(1/2)x + 4

For illustration purposes, lets add the line with slope of 2 that goes through points (4,0) and (0,-8): y = 2x -8

See the attached graph.

Write the​ slope-intercept equation of the function f whose graph satisfies the given-example-1
User Vinay Joseph
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