Question

function a is a linear function. an equation for function a is $y = 4 - 2x$. function b is also a linear function. some values of function b are shown in the table:

$x$	$-3$	$0$	$3$
$y$	$-1$	$-1$	$-1$

compare the functions by completing the sentences.
options: greater than, less than, equal to
the slope of function a is the slope of function b. the $y$-intercept of function a is the $y$-intercept of function b.

Explanation:

Step1: Find slope of Function A

The equation of Function A is \( y = 4 - 2x \), which is in the form \( y = mx + b \) (where \( m \) is slope and \( b \) is y - intercept). So, slope of Function A (\( m_A \)) is \( - 2 \).

Step2: Find slope of Function B

For a linear function, slope \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Using points from Function B's table, say \( (x_1,y_1)=(-3,-1) \) and \( (x_2,y_2)=(0,-1) \). Then \( m_B=\frac{-1 - (-1)}{0 - (-3)}=\frac{0}{3}=0 \).

Step3: Compare slopes

Since \( - 2<0 \), the slope of Function A is less than the slope of Function B.

Step4: Find y - intercept of Function A

From \( y = 4 - 2x \), y - intercept of Function A (\( b_A \)) is \( 4 \).

Step5: Find y - intercept of Function B

For Function B, when \( x = 0 \), \( y=-1 \). So, y - intercept of Function B (\( b_B \)) is \( - 1 \).

Step6: Compare y - intercepts

Since \( 4>-1 \), the y - intercept of Function A is greater than the y - intercept of Function B.

Answer:

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