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
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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.
