Question

function a and function b are linear functions.
function a
x | y
-8 | -11
2 | 9
4 | 13
function b
$y = x$
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 \((-8, -11)\) and \((2, 9)\). Slope \(m = \frac{y_2 - y_1}{x_2 - x_1}=\frac{9 - (-11)}{2 - (-8)}=\frac{20}{10}=2\).

Step2: Find equation of Function A

Using point - slope form \(y - y_1 = m(x - x_1)\) with \((2, 9)\) and \(m = 2\):
\(y - 9 = 2(x - 2)\)
\(y - 9 = 2x - 4\)
\(y = 2x + 5\). So y - intercept of A is \(5\).

Step3: Find y - intercept of Function B

Function B: \(y = x\), in slope - intercept form \(y=mx + b\), \(b = 0\) (y - intercept is \(0\)).

Step4: Compare y - intercepts

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

Answer:

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