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Write a linear function with the given values: f(-4) =2, f(6) = -3

User Abdfahim
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Final answer:

To write a linear function with the given values of f(-4) = 2 and f(6) = -3, we calculate the slope (m) as -0.5 and the y-intercept (b) as 0. The linear function is f(x) = -0.5x.


Step-by-step explanation:

To write a linear function with the given values, we need to find the slope (m) and the y-intercept (b).

Using the point-slope form of a linear equation, we can calculate the slope as:

m = (f(6) - f(-4)) / (6 - (-4))

Substituting the values f(6) = -3 and f(-4) = 2, we get:

m = (-3 - 2) / (6 - (-4)) = -5 / 10 = -0.5

Now, we can use the slope-intercept form of a linear equation to find the function:

f(x) = mx + b

Using the point (-4, 2), we can substitute the values for x and f(x) to solve for b:

2 = -0.5 * (-4) + b

Simplifying, we find:

2 = 2 + b

Subtracting 2 from both sides, we get:

b = 0

Therefore, the linear function is:

f(x) = -0.5x

Learn more about writing linear function

User Allan Elder
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