Question

If f ( x ) f ( x ) is a linear function, f ( − 5 ) = 0 f ( - 5 ) = 0 , and f ( 2 ) = 4 f ( 2 ) = 4 , find an equation for f ( x ) f ( x )
f(x)=________

Answer 1

Answer:   f(x) = (4/7)x + 20/7

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Explanation:

We have

f(-5) = 0 and f(2) = 4

This means the two points (-5,0) and (2,4) are on this line

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Find the slope of the line through (x1,y1) = (-5,0) and (x2,y2) = (2,4)

m = (y2 - y1)/(x2 - x1)

m = (4 - 0)/(2 - (-5))

m = (4 - 0)/(2 + 5)

m = 4/7 is the slope

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Plug m = 4/7 and (x1,y1) = (-5,0) into the point-slope formula. Solve for y.

y - y1 = m(x - x1)

y - 0 = (4/7)(x - (-5))

y = (4/7)(x + 5)

y = (4/7)x + (4/7)*5

y = (4/7)x + 20/7

f(x) = (4/7)x + 20/7

This linear equation has a slope of 4/7 and a y intercept of 20/7.

Answer 2

Answer:

f(x) = 4/7x + 20/7

Step-by-step explanation:

If we were to graph this function, we would see that the two points would be, (-5, 0), and (2, 4). First, we have to find the slope, which is equal to:

(first y-coordinate - the second y coordinate)

(first x-coordinate - second x coordinate)

= (0 - 4)

   (-5 - 2)

= -4/-7 = 4/7. now, we multiple -5 by 4/7 and get -20/7. we have to add 20/7.

Thus, the answer is f(x) = 4/7x + 20/7