SOLUTION: Write the slope-intercept equation of the function f whose graph satisfies the given conditions. The graph of f passes through (- 4, 9) and is perpendicular to the line that has an

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Write the slope-intercept equation of the function f whose graph satisfies the given conditions. The graph of f passes through (- 4, 9) and is perpendicular to the line that has an      Log On


   



Question 1204121: Write the slope-intercept equation of the function f whose graph satisfies the given conditions. The graph of f passes through (- 4, 9) and is perpendicular to the line that has an x-intercept of 7 and a y-intercept of 14.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

the slope-intercept equation of the function is:
+y=mx%2Bb+
where++m is a slope and +b is y-intercept
The graph of f passes through (+-+4, +9)
+9=m%28-4%29%2Bb+
+9=-4m%2Bb+

is perpendicular to the line that has an +x-intercept of++7 and a +y-intercept of +14
so, points are:
x-intercept at (+7,+0)
y-intercept at (+0,+14)
we will find a slope
+m=%2814-0%29%2F%280-7%29=14%2F-7=-2
since this line is perpendicular to the line we are looking for, then a slope of our line will be negative reciprocal of++m+=-2 and it is +-1%2F-2=1%2F2
going back to
+9=-4m%2Bb ....substitute slope
+9=-4%281%2F2%29%2Bb+
+9=-2%2Bb+
+b=9%2B2
+b=11
now we have a slope and +y-intercept, so our line is:
+y=%281%2F2%29x%2B11