Question

Use the image to answer the question.
An illustration of a coordinate plane with four quadrants shows the x and y axes extending from negative 5 to 5 in increments of 1. An upward slanting line is plotted on the coordinate plane. The upward slanting line with arrows at both ends passes through the following closed points: left parenthesis negative 4 comma start fraction negative 10 over 3 end fraction right parenthesis, and left parenthesis negative 1 comma start fraction negative 4 over 3 end fraction right parenthesis.

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

(1 point)
Responses

The initial value is −23
, and the rate of change is 23
.
The initial value is negative Start Fraction 2 over 3 End Fraction , and the rate of change is Start Fraction 2 over 3 End Fraction .

The initial value is 16
, and the rate of change is 32
.
The initial value is Start Fraction 1 over 6 End Fraction , and the rate of change is Start Fraction 3 over 2 End Fraction .

The initial value is −2
, and the rate of change is 23
.
The initial value is negative 2 , and the rate of change is Start Fraction 2 over 3 End Fraction .

The initial value is 23
, and the rate of change is −23
.

Answer 1

Slope = (−4/3 − (−10/3)) / (−1 − (−4)) = (6/3)/3 = 2/3.
y-intercept: using (−1, −4/3), −4/3 = (2/3)(−1) + b → b = −4/3 + 2/3 = −2/3.

So the initial value is −2/3 and the rate of change is 2/3.