Question

function a and function b are linear functions.
function a

x	y
-4	-20
-3	-15
1	5

function b
graph of function b
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 y-intercept of Function A

The general form of a linear function is \( y = mx + b \), where \( b \) is the y-intercept. First, find the slope \( m \) of Function A using two points, e.g., \((-4, -20)\) and \((-3, -15)\). The slope formula is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). So \( m=\frac{-15 - (-20)}{-3 - (-4)}=\frac{5}{1} = 5 \). Now use point \((1, 5)\) in \( y = mx + b \): \( 5 = 5(1)+b \), so \( b = 0 \). Thus, y-intercept of Function A is \( 0 \).

Step2: Find y-intercept of Function B

From the graph of Function B, the line crosses the y-axis at \( (0, 5) \) (since when \( x = 0 \), \( y = 5 \)). So the y-intercept of Function B is \( 5 \).

Step3: Compare y-intercepts

Function A's y-intercept is \( 0 \), Function B's is \( 5 \). So \( 0 < 5 \), meaning y-intercept of A is less than B's.

Answer:

The \( y \)-intercept of Function A is less than the \( y \)-intercept of Function B.