Question

Write a linear function f with f(−4)=2 and

f(6)=−3.
a) f(x)=− 1/2x+4
b) f(x)= 1/2 x−5
c) f(x)=− 1/2 x−4
d) f(x)= 1/2 x+5

Answer 1

To find the correct linear function, we calculate the slope with the given points, which is -1/2. After that, we use one of the given points and the point-slope formula to establish the linear equation, resulting in f(x) = -1/2 x - 4.

Step-by-step explanation:

Write a Linear Function Based on Given Points

To write a linear function f(x) with the given values of f(−4)=2 and f(6)=−3, we can use the point-slope form of a line equation, which is y - y1 = m(x - x1), where m is the slope, and (x1, y1) is a point on the line. First, we calculate the slope using the formula m = (y2 - y1) / (x2 - x1).

The slope is calculated as follows:

m = (-3 - 2) / (6 - (-4)) = -5 / 10 = -1/2

Now that we have the slope, we can choose one of the points to write the equation. Let's use the point (−4, 2).

y - 2 = (-1/2)(x - (-4))

Expanding this, we get:

y - 2 = (-1/2)x - 2

Adding 2 to both sides to solve for y, we get:

y = (-1/2)x

Therefore, the correct option is c) f(x) = -1/2 x - 4.