Answer:
- f(x) = 3x +4
- f(x) = 5x +2
- f(x) = -4x +11
- f(x) = -4x +11 (same table as problem 3)
Explanation:
To write the equation for f(x) in slope-intercept form, you need to know the slope and the y-intercept. The y-intercept is the value of f(x) when x=0. You can read this directly from the table.
The slope is the ratio of the change in f(x) to the change in x. It can be computed using the formula ...
m = (y2 -y2)/(x2 -x1)
where (x1, y1) and (x2, y2) are any two pairs of numbers from the table. You can use the first two table rows, for example.
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1. m = (10 -4)/(3 -0) = 6/3 = 2; y-intercept = 4 (from ordered pair (0, 4))
y = mx +b . . . . line with slope m and y-intercept b
f(x) = 2x +4
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2. m = (2 -(-3))/(0 -(-1)) = 5/1 = 5
f(x) = 5x +2
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3. m = (11 -19)/(0 -(-2)) = -8/2 = -4
f(x) = -4x +11
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4. same as 3.