Answer:
y = -0.5x + 5.5
Explanation:
A linear function can be represented in the form of y = mx + b, where m is the slope and b is the y-intercept. The slope of a line is the ratio of the change in y to the change in x (rise over run) and the y-intercept is the point where the line crosses the y-axis.
To find the rule for this linear function, we can use the two points (x1, y1) and (x2, y2) to find the slope m:
m = (y2 - y1) / (x2 - x1)
If we use the points (7, 2) and (5, 3) to find the slope, we have:
m = (3 - 2) / (5 - 7) = 1 / (-2) = -0.5
We can also use the point (x1, y1) to find the y-intercept b:
b = y1 - m * x1
If we use the point (7, 2) to find the y-intercept, we have:
b = 2 - (-0.5) * 7 = 2 + 3.5 = 5.5
So the rule for the linear function is:
y = -0.5x + 5.5
We can confirm this rule by checking the point (x=-1,y=6)
y = -0.5(-1) + 5.5 = 6