Question

I will list some graphed points:
(-1, -4/3), (4, -10/3)

Determine the initial value and the rate of change of the linear function as given in the graph.

Answer 1

To find the initial value and rate of change of the linear function, we can use the formula for a linear function in slope-intercept form: y = mx + b, where m is the rate of change (slope) and b is the initial value (y-intercept).

Using the two points (-1, -4/3) and (4, -10/3), we can find the slope (rate of change) using the formula:

m = (y2 - y1) / (x2 - x1)

Plugging in the values, we get:

m = (-10/3 - (-4/3)) / (4 - (-1))
m = (-10/3 + 4/3) / (4 + 1)
m = (-6/3) / 5
m = -2/5

The slope of the linear function is -2/5.

To find the initial value (y-intercept), we can plug in one of the points into the equation and solve for b.

Using the point (-1, -4/3):

-4/3 = (-2/5)(-1) + b
-4/3 = 2/5 + b
-4/3 - 2/5 = b
(-20/15) - (6/15) = b
-26/15 = b

The initial value (y-intercept) is -26/15.

Therefore, the linear function with the given graph has an initial value of -26/15 and a rate of change (slope) of -2/5.