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.
m is the slope of the line(slope of f)
and is a point on the line.
Here, m = -1/2 and = (-6, 9) .
So, equation of line f is
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