Question

function 3\
y = -3x - 5\
function 4\
the slope is 2 and the\
y-intercept is 1.\
answer the following questions.\
(a) which functions have graphs with slopes less than 3?\
(check all that apply.)\
☑️ 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 function has the graph with a y-intercept closest to 0?\
⚪️ function 1 ⚪️ function 2 ⚪️ function 3 ⚪️ function 4

Explanation:

Step1: Find Function1 slope/intercept

Identify 2 points on Function1: $(0, 12)$ and $(2, 8)$.
Slope: $m_1=\frac{8-12}{2-0}=-2$
Y-intercept: $b_1=12$

Step2: Find Function2 slope/intercept

Use given points: $(2, 6)$ and assume y-intercept from context (calculate slope first, then intercept). Let's take another point implied: when $x=0$, $y=0$ (since slope $m_2=\frac{6-0}{2-0}=3$).
Slope: $m_2=3$
Y-intercept: $b_2=0$

Step3: List Function3 slope/intercept

From $y=-3x-5$:
Slope: $m_3=-3$
Y-intercept: $b_3=-5$

Step4: List Function4 slope/intercept

From description:
Slope: $m_4=2$
Y-intercept: $b_4=1$
---

Part (a) Check slopes < 3

Step5: Compare slopes to 3

$m_1=-2<3$, $m_2=3
ot<3$, $m_3=-3<3$, $m_4=2<3$

Part (b) Find largest y-intercept

Step6: Compare y-intercepts

$b_1=12$, $b_2=0$, $b_3=-5$, $b_4=1$. Largest is 12.

Part (c) Find intercept closest to 0

Step7: Calculate distance from 0

$|b_1|=12$, $|b_2|=0$, $|b_3|=5$, $|b_4|=1$. Closest is 0.

Answer:

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