Question

function a is a linear function. some values of function a are shown in the table.
x | 0 | 4 | 6
y | 1 | -7 | -11
function b is also a linear function with a y-intercept of 4.5 and an x-intercept of 9.
compare the functions by completing the table.

	greater for function a	greater for function b	same for both
y-intercept
slope

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not feeling ready yet? this can help:
compare linear functions: tables, graphs, and equations (64)

Explanation:

Step1: Find y-intercept of Function A

For a linear function \( y = mx + b \), the y-intercept \( b \) is the value of \( y \) when \( x = 0 \). From Function A's table, when \( x = 0 \), \( y = 1 \). So y-intercept of A is \( 1 \). Function B's y-intercept is \( 4.5 \). So \( 4.5>1 \), y-intercept is greater for B.

Step2: Calculate slope of Function A

Slope \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Take points \( (0,1) \) and \( (4, -7) \). \( m_A=\frac{-7 - 1}{4 - 0}=\frac{-8}{4}=-2 \).

Step3: Calculate slope of Function B

Function B has y-intercept \( b = 4.5 \) and x-intercept \( 9 \) (so point \( (9,0) \)). Slope \( m_B=\frac{0 - 4.5}{9 - 0}=\frac{-4.5}{9}=-0.5 \).

Step4: Compare slopes

\( m_A=-2 \), \( m_B = - 0.5 \). Since \( -0.5>-2 \), slope is greater for B.

Answer:

• y - intercept: Greater for Function B
• Slope: Greater for Function B