Use the table to answer the question.

Question

x
y

−5
8
−7
14
Determine the rate of change and the initial value of the linear function given here as a table of values.

(1 point)
Responses

m=−7, b=−3
m equals negative 7 comma b equals negative 3

m=−0.5, b=5.5
m equals negative 0.5 comma b equals 5.5

m=−0.5, b=10.5
m equals negative 0.5 comma b equals 10.5

m=−3, b=−7

Answer 1

To determine the rate of change (slope) and the initial value (y-intercept) of the linear function based on the provided table, we can follow these steps:

1. Calculate the slope (m): The slope can be calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Using the points \((-5, 8)\) and \((-7, 14)\):

   • \(y_1 = 8\), \(y_2 = 14\)
   • \(x_1 = -5\), \(x_2 = -7\)

   Substituting: \[ m = \frac{14 - 8}{-7 - (-5)} = \frac{6}{-2} = -3 \]

2. Find the initial value (b): The equation of a linear function is \(y = mx + b\). We can use one of the points to find b. Let’s use the point \((-5, 8)\): \[ 8 = -3(-5) + b \] \[ 8 = 15 + b \] \[ b = 8 - 15 = -7 \]

Thus, the rate of change (m) is \(-3\) and the initial value (b) is \(-7\).

So, the correct response is: m=−3, b=−7.