Questions: Function A and Function B are linear functions. Function A Function B ------------------------ y=1/2 x-1 x y ------------------------ -8 -1 -4 0 8 3 Select all the statements that are true. The y-intercept of Function A is equal to the y-intercept of Function B. The y-intercept of Function A is greater than the y-intercept of Function B. The slope of Function A is greater than the slope of Function B. The slope of Function A is less than the slope of Function B.

Solution Steps

To find the equation of Function B, we need to determine its slope and y-intercept. We have three points from the table: \((-8, -1)\), \((-4, 0)\), and \( (8, 3) \).

First, calculate the slope \(m\) using the formula:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Using points \((-8, -1)\) and \((-4, 0)\):

\[ m = \frac{0 - (-1)}{-4 - (-8)} = \frac{1}{4} \]

Now, use the point-slope form \(y - y_1 = m(x - x_1)\) to find the y-intercept. Using point \((-4, 0)\):

\[ y - 0 = \frac{1}{4}(x - (-4)) \]

\[ y = \frac{1}{4}x + 1 \]

Thus, the equation of Function B is:

\[ y = \frac{1}{4}x + 1 \]

The y-intercept of Function A is \(-1\) (from \(y = \frac{1}{2}x - 1\)).

The y-intercept of Function B is \(1\) (from \(y = \frac{1}{4}x + 1\)).

The slope of Function A is \(\frac{1}{2}\).

The slope of Function B is \(\frac{1}{4}\).

Final Answer