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Write a linear equation in slope-intercept form with the values f(0) = 4 and f (2) = -6.

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Final answer:

To write the linear equation in slope-intercept form, we need to calculate the slope using the given points and then substitute the slope and one of the points into the equation. The equation is y = -5x + 4.

Step-by-step explanation:

To write a linear equation in slope-intercept form, we need to use the given information: f(0) = 4 and f(2) = -6. In the slope-intercept form, the equation is written as y = mx + b, where m is the slope and b is the y-intercept.

Step 1: Calculate the slope (m). Using the formula for slope:
m = (y2-y1) / (x2-x1). Plugging in the values y2 = -6, y1 = 4, x2 = 2, and x1 = 0, we get:
m = (-6-4) / (2-0) = -10/2 = -5.

Step 2: Substitute the slope (m) and one of the points (0, 4) into the equation. We have: y = -5x + b. Plugging in the values x = 0 and y = 4, we solve for b:
4 = -5(0) + b
4 = b.

Therefore, the linear equation in slope-intercept form is y = -5x + 4.

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