Final answer:
To write the two linear functions, we calculate the slopes from the given points, then use one of the points with the slope to find the y-intercepts. The first function is f(x) = -x + 3, and the second is f(x) = -0.8x - 4.
Step-by-step explanation:
Writing a linear function that corresponds to the given values involves finding the slope and intercept of the line. To find the slope (m), we can use the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.
For the first linear function, using the points (-2, 5) and (6, -3), the slope calculates to:
m = (-3 - 5) / (6 - (-2)) = (-8) / (8) = -1
Now that we have the slope, we need to find the y-intercept (b). Using the point-slope form y - y1 = m(x - x1) and plugging in one of the points:
5 - (-1)(-2) = -1 * x + b
5 - 2 = -x + b
3 = -x + b
Thus, the y-intercept is b = 3. So the equation of the first linear function is f(x) = -x + 3.
For the second linear function, using the points (0, -4) and (10, -12), the slope calculates to:
m = (-12 - (-4)) / (10 - 0) = (-8) / (10) = -0.8
Since the line crosses the y-axis at (0, -4), the y-intercept is -4. Thus, the equation of the second linear function is f(x) = -0.8x - 4.