Answer:
Explanation:
To write a linear function for a given set of points, we can use the slope-intercept form of the equation, which has the form f(x) = mx + b. The coefficient m is the slope of the line and the constant b is the y-intercept, where the line crosses the y-axis.
To find the slope m of the line, we can use the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are any two points on the line. For example, we can use the points (-2, -6) and (-1, -2.5) to find the slope:
m = (y2 - y1) / (x2 - x1) = (-2.5 - (-6)) / (-1 - (-2)) = 3.5 / 1 = 3.5
Now that we know the slope, we can use any of the given points to find the y-intercept b. For example, we can use the point (0, 1):
f(x) = mx + b
1 = 3.5 * 0 + b
b = 1
Therefore, the linear function that passes through the given points is:
f(x) = 3.5x + 1
Note that we could also have used any of the other points to find the y-intercept, and we would have arrived at the same result.