Question

Write a linear function $f$ with $f\left(-4\right)=2$ and $f\left(6\right)=-3$ .

Answer 1

To write a linear function given two points, find the slope using the formula (y2 - y1) / (x2 - x1), and then use the point-slope form of a linear function to write the equation.

Step-by-step explanation:

To write a linear function given two points, we first need to find the slope of the line. The slope is given by the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. In this case, the two points are (-4, 2) and (6, -3). Plugging these values into the formula, we get m = (-3 - 2) / (6 - (-4)) = -5/10 = -1/2.

Once we have the slope, we can use the point-slope form of a linear function, which is y - y1 = m(x - x1). Plugging in the values from one of the points, let's say (-4, 2), we get y - 2 = -1/2(x - (-4)). Simplifying this equation, we get y - 2 = -1/2(x + 4).

Thus, the linear function is f(x) = -1/2(x + 4) + 2.

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