If f is a linear function, with f ( − 5 ) = 2 and f ( 7 ) = − 7 , find an equation for the function in slope-intercept form. f ( x ) =

Question

Please  help i cannot figure this out

Answer 1

Slope=(f(-5)-f(7))/(-5-7)=(2-(-7))/-12=-9/12=-¾.

Now we have the slope, we can write:

f(x)-f(-5)=-¾(x-(-5)),

f(x)-2=-¾(x+5),

f(x)-2=-3x/4-15/4,

f(x)=-3x/4-15/4+2,

f(x)=-3x/4-7/4.

Or we could use the other point (7,f(7))=(7,-7):

f(x)-f(7)=-¾(x-7),

f(x)-(-7)=-3x/4+21/4,

f(x)+7=-3x/4+21/4,

f(x)=-3x/4+21/4-7,

f(x)=-3x/4-7/4.

If you find f(x), f(-5), f(7) confusing, then use y=f(x).

This gives you the points (-5,2) and (7,-7) from which you can find the slope. Then replace f(x) with y when you work out the equation of the line joining the points.