Question

function 1\
(graph of a line on a coordinate plane)\
function 2\

x	y	\
-2	6	\
-1	5	\
0	4	\
1	3	\
2	2	\

function 3\
$y = 5x + 1$\
function 4\
the slope is 2 and the $y$-intercept is $-3$.\
answer the following questions.\
(a) which function’s graph is the steepest?\
\bigcirc function 1 \bigcirc function 2 \bigcirc function 3 \bigcirc function 4\
(b) which functions have graphs with $y$-intercepts greater than $-4$? (check all that apply.)\
function 1 \quad function 2 \quad function 3 \quad function 4\
(c) which function has the graph with a $y$-intercept farthest from 0?\
function 1 \quad function 2 \quad function 3 \quad function 4

Explanation:

Step1: Find slopes of all functions

• Function 1: Use points $(-2,0)$ and $(0,-10)$. Slope $m_1=\frac{-10-0}{0-(-2)}=\frac{-10}{2}=-5$, $|m_1|=5$
• Function 2: Use points $(0,4)$ and $(1,3)$. Slope $m_2=\frac{3-4}{1-0}=-1$, $|m_2|=1$
• Function 3: Slope $m_3=5$, $|m_3|=5$
• Function 4: Slope $m_4=2$, $|m_4|=2$

Step2: Find y-intercepts of all functions

• Function 1: Graph crosses y-axis at $(0,-10)$, so $b_1=-10$
• Function 2: Table has $(0,4)$, so $b_2=4$
• Function 3: Equation $y=5x+1$, so $b_3=1$
• Function 4: Given $b_4=-3$

Step3: Answer (a): Compare absolute slopes

Largest absolute slope is 5 (Function 1 and 3)

Step4: Answer (b): Check $b>-4$

$b_2=4>-4$, $b_3=1>-4$, $b_4=-3>-4$; $b_1=-10<-4$

Step5: Answer (c): Distance from 0

$|b_1|=|-10|=10$, $|b_2|=4$, $|b_3|=1$, $|b_4|=3$. Largest distance is 10 (Function 1)

Answer:

(a) Function 1, Function 3
(b) Function 2, Function 3, Function 4
(c) Function 1