Question

part a
mal is creating an input/output table for a linear function. enter a number in each box to complete the table.

input\toutput
-6\t-22
-4\t-16
-1\t
5\t
\t32

part b
choose all linear functions with a slope that is greater than jamal’s linear function.
a ( y = 6 )\tb ( y = 5x )
c ( y = -4x )\td ( y = 4x + 3 )
e ( y = x + 10 )\tf ( y = \frac{8}{3}x + 4 )

Explanation:

Step1: Find slope of linear function

Slope $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-16 - (-22)}{-4 - (-6)} = \frac{6}{2} = 3$

Step2: Find y-intercept $b$

Use $x=-6, y=-22$: $-22 = 3(-6) + b$
$-22 = -18 + b$
$b = -22 + 18 = -4$
Function: $y = 3x - 4$

Step3: Calculate output for $x=-1$

$y = 3(-1) - 4 = -3 - 4 = -7$

Step4: Calculate output for $x=5$

$y = 3(5) - 4 = 15 - 4 = 11$

Step5: Calculate input for $y=32$

$32 = 3x - 4$
$3x = 32 + 4 = 36$
$x = \frac{36}{3} = 12$

Step6: Compare slopes for Part B

Jamal's slope is 3. Check each option:

• A: $y=6$, slope $0 < 3$
• B: $y=5x$, slope $5 > 3$
• C: $y=-4x$, slope $-4 < 3$
• D: $y=4x+3$, slope $4 > 3$
• E: $y=x+10$, slope $1 < 3$
• F: $y=\frac{8}{3}x+4$, slope $\frac{8}{3} \approx 2.67 < 3$

Answer:

Part A Completed Table:

Input	Output
-4	-16
-1	-7
5	11
12	32

Part B Selected Options:

B. $y=5x$
D. $y=4x+3$