Question

Two linear functions are shown below.

Function A: y = 8x - 2

Function B:
x -1 0 1 2
y -2 -1 0 1


Which statement is true?
Responses
A The y-intercept of function A is equal to the y-intercept of Function B.The y -intercept of function A is equal to the y -intercept of Function B.
B The y-intercept of function A is less than the y-intercept of Function B.The y -intercept of function A is less than the y -intercept of Function B.
C The y-intercept of function A is greater than the y-intercept of Function B.The y -intercept of function A is greater than the y -intercept of Function B.
D The rate of change for Function A is equal to the rate of change for function B.

Answer 1

To determine which statement is true, we need to find the y-intercepts of both functions and compare their rates of change.

**For Function A:**
The equation is given as \(y = 8x - 2\). The y-intercept occurs when \(x = 0\):
\[
y = 8(0) - 2 = -2
\]
So, the y-intercept of Function A is \(-2\).

**For Function B:**
We have the table of values:
- When \(x = -1\), \(y = -2\)
- When \(x = 0\), \(y = -1\)
- When \(x = 1\), \(y = 0\)
- When \(x = 2\), \(y = 1\)

The y-intercept for Function B is also when \(x = 0\):
\[
y = -1
\]

**Comparison of y-intercepts:**
- Function A has a y-intercept of \( -2 \).
- Function B has a y-intercept of \( -1 \).

Thus:
\(-2 < -1\), meaning the y-intercept of Function A is less than the y-intercept of Function B.

**Rate of Change:**
The rate of change (slope) of Function A can be determined from its equation \(y = 8x - 2\). The slope is \(8\).

For Function B, we can find the slope using any two points from the table. For example, using points (0, -1) and (1, 0):
\[
\text{slope} = \frac{0 - (-1)}{1 - 0} = \frac{1}{1} = 1
\]

**Conclusion:**
- The y-intercepts are \(-2\) for Function A and \(-1\) for Function B, so the y-intercept of Function A is less than that of Function B.
- The rates of change are \(8\) for Function A and \(1\) for Function B, which are not equal.

Therefore, the correct statement is:

**B. The y-intercept of function A is less than the y-intercept of Function B.**