Question

four different linear functions are represented below.
function 1 (graph)
function 2

x	y
-2	7
-1	3
0	-1
1	-5
2	-9

function 3
$y = 3x - 4$
function 4
the slope is 1 and the y - intercept is 2.
answer the following questions.
(a) which function’s graph is the least steep?
○ function 1 ○ function 2 ○ function 3 ○ function 4
(b) which function has the graph with the greatest y - intercept?
○ function 1 ○ function 2 ○ function 3 ○ function 4
(c) which functions have graphs with slopes less than -3?
(check all that apply.)
function 1 function 2 function 3 function 4

Explanation:

Step1: Find slopes of all functions

• Function 1: Use points (0,6) and (2,0). Slope $m_1=\frac{0-6}{2-0}=-3$
• Function 2: Use points (0,-1) and (1,-5). Slope $m_2=\frac{-5-(-1)}{1-0}=-4$
• Function 3: From $y=3x-4$, slope $m_3=3$
• Function 4: Given slope $m_4=1$

Step2: Find y-intercepts of all functions

• Function 1: Graph crosses y-axis at (0,6), so $b_1=6$
• Function 2: Table shows $x=0, y=-1$, so $b_2=-1$
• Function 3: From $y=3x-4$, $b_3=-4$
• Function 4: Given y-intercept $b_4=2$

Step3: Answer (a): Compare slope magnitudes

Steepness = $|m|$:
$|m_1|=3$, $|m_2|=4$, $|m_3|=3$, $|m_4|=1$. Smallest magnitude is 1.

Step4: Answer (b): Compare y-intercepts

$b_1=6$, $b_2=-1$, $b_3=-4$, $b_4=2$. Largest value is 6.

Step5: Answer (c): Check slopes < -3

$m_1=-3$ (not < -3), $m_2=-4$ ( < -3), $m_3=3$ (not < -3), $m_4=1$ (not < -3). Only Function 2 qualifies.

Answer:

(a) Function 4
(b) Function 1
(c) Function 2