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Write a linear function f(x) = mx + b for the graph.
(-2,-6) (-1,-2.5) (0,1) (1,4.5)

User Mneumann
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Answer:

Explanation:

To write a linear function for a given set of points, we can use the slope-intercept form of the equation, which has the form f(x) = mx + b. The coefficient m is the slope of the line and the constant b is the y-intercept, where the line crosses the y-axis.

To find the slope m of the line, we can use the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are any two points on the line. For example, we can use the points (-2, -6) and (-1, -2.5) to find the slope:

m = (y2 - y1) / (x2 - x1) = (-2.5 - (-6)) / (-1 - (-2)) = 3.5 / 1 = 3.5

Now that we know the slope, we can use any of the given points to find the y-intercept b. For example, we can use the point (0, 1):

f(x) = mx + b

1 = 3.5 * 0 + b

b = 1

Therefore, the linear function that passes through the given points is:
f(x) = 3.5x + 1

Note that we could also have used any of the other points to find the y-intercept, and we would have arrived at the same result.

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