The points on the graph are (-4,-10/3) and (-1,-4/3) Determan the initial value and rate change
To determine the initial value and rate of change, we can use the slope-intercept form of a linear equation, which is given by:
y = mx + b
where m is the rate of change (slope), and b is the initial value (y-intercept).
First, let's find the rate of change (m) using the two given points (-4, -10/3) and (-1, -4/3):
m = (y2 - y1) / (x2 - x1)
m = (-4/3 - (-10/3)) / (-1 - (-4))
m = (-4/3 + 10/3) / (-1 + 4)
m = (6/3) / (3)
m = 2
So the rate of change (slope) is 2.
Now, let's find the initial value (b). We can substitute one of the points into the slope-intercept form:
-4/3 = 2(-1) + b
-4/3 = -2 + b
b = -4/3 + 2
b = -4/3 + 6/3
b = 2/3
So the initial value (y-intercept) is 2/3.
Therefore, the equation of the line is y = 2x + 2/3.