To determine the rate of change and initial value, we can use the formula for the equation of a line: y = mx + b, where m represents the rate of change and b represents the initial value (y-intercept).
Using the given points (2, 22) and (8, 25), we can find the equation of the line that passes through these points.
First, we need to find the slope (rate of change) by using the formula:
m = (y2 - y1) / (x2 - x1)
Plugging in the values from the given points:
m = (25 - 22) / (8 - 2)
= 3 / 6
= 1/2
So, the rate of change (slope) is 1/2.
Next, we need to find the initial value (y-intercept), b. We can choose any of the given points to substitute into the equation y = mx + b.
Using the point (2,22):
22 = (1/2)(2) + b
22 = 1 + b
b = 22 - 1
b = 21
Therefore, the initial value (y-intercept) is 21.
The equation of the line that passes through the given points is y = (1/2)x + 21.
So, the rate of change is 1/2 and the initial value is 21.
The points on the graph are: (2,22) and (8,25)
Determan the rate of change and initial value.
1 answer
1 answer