Question

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Slope and y-intercepts Quick Check
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Question
Find the initial value of the linear function, given that the rate of change is m=−4/7
, and (14,3)
is an (x,y)
value of the linear function.(1 point)
Responses

b=11
b equals 11

b=15.71
b equals 15.71

b=−5
b equals negative 5

b=12.29

Answer 1

To find the initial value (y-intercept, \( b \)) of the linear function given the rate of change (slope, \( m \)) and a point on the line \((x, y)\), we can use the point-slope form of the linear equation:

\[ y = mx + b \]

Given:
- Slope \( m = -\frac{4}{7} \)
- Point \( (x, y) = (14, 3) \)

We can plug in the values into the equation:

1. Substitute \( m \), \( x \), and \( y \):
\[
3 = -\frac{4}{7}(14) + b
\]

2. Calculate \( -\frac{4}{7}(14) \):
\[
-\frac{4}{7} \times 14 = -\frac{56}{7} = -8
\]

3. Now substitute this back into the equation:
\[
3 = -8 + b
\]

4. Solve for \( b \):
\[
b = 3 + 8
\]
\[
b = 11
\]

So, the initial value (y-intercept) of the linear function is \( b = 11 \).

The correct response is:
**b = 11**.