Question

function a and function b are linear functions. function a has a table with x and y values: x=-4, y=-3; x=-3, y=-1; x=5, y=15. function b is y = 3x. which statement is true? the y-intercept of function a is greater than the y-intercept of function b. the y-intercept of function a is less than the y-intercept of function b.

Explanation:

Step1: Find slope of Function A

Use two points \((-4, -3)\) and \((-3, -1)\). Slope \(m = \frac{y_2 - y_1}{x_2 - x_1}=\frac{-1 - (-3)}{-3 - (-4)}=\frac{2}{1}=2\).

Step2: Find equation of Function A

Using point - slope form \(y - y_1 = m(x - x_1)\) with \((-4, -3)\) and \(m = 2\):
\(y - (-3)=2(x - (-4))\)
\(y + 3 = 2(x + 4)\)
\(y+3 = 2x + 8\)
\(y = 2x+5\). So y - intercept of Function A is \(5\).

Step3: Find y - intercept of Function B

Function B: \(y = 3x\), in the form \(y=mx + b\) (where \(b\) is y - intercept), so y - intercept of Function B is \(0\).

Step4: Compare y - intercepts

Since \(5>0\), y - intercept of Function A (\(5\)) is greater than y - intercept of Function B (\(0\)).

Answer:

The y - intercept of Function A is greater than the y - intercept of Function B.