# Slope Intercept Equation -6, 9

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parjzna12512

Mathematics

### Question Description

Write the slope intercept equation of the function f whose graph satisfies the given conditions.

The graph of f passes through (-6, 9) and is perpendicular to the line that has an x-intercept of 1 and a y-intercept of -2

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Equation of line in slope intercept form is

y = mx + b

where m is the slope and b is the y-intercept.

The line which is perpendicular to f has y-intercept of -2.

Therefore, b = -2

So, equation of the perpendicular line is

y = mx - 2

Also its x-intercept is 1. So, substitute x = 1 and y = 0 in the equation.

0 = m*1 - 2

0 = m - 2

m = 2

So equation of the perpendicular line becomes

y = 2x - 2

Since f is perpendicular to the above line,

slope of f = -1/m = -1/2

Also f passes through (-6, 9).

Now we can use the point slope form of line to find equation of f.

$y-y_0=m(x-x_0)\\ \\$

m is the slope of the line(slope of  f)

and $(x_0,y_0)$ is a point on the line.

Here, m = -1/2 and $(x_0,y_0)$ = (-6, 9) .

So, equation of line f is

$y-9=\frac{-1}{2}(x-(-6))\\ \\ y-9=\frac{-1}{2}(x+6)\\ \\ y-9=\frac{-1}{2}x-\frac{1}{2}\times6\\ \\ y=\frac{-1}{2}x-3+9\\ \\ y=\frac{-1}{2}x+6\\$

fulnzanve3 (279)
Rice University
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Anonymous
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