Question

function 1
(graph of a line)
function 2

x	y
-2	-10
-1	-6
0	-2
1	2
2	6

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

Explanation:

Step1: Find slope of Function 1

Identify two points on the line, e.g., $(0, 3)$ and $(3, 0)$. Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{0-3}{3-0}=-1$

Step2: Find slope of Function 2

Use two table points, e.g., $(0, -2)$ and $(1, 2)$.
$m=\frac{2-(-2)}{1-0}=4$

Step3: Identify slope of Function 3

From $y=-3x-5$, slope $m=-3$

Step4: Identify slope of Function 4

Given slope $m=2$

Step5: Answer part (a)

Compare slopes to 3: $-1<3$, $4>3$, $-3<3$, $2<3$. So Functions 1,3,4 qualify.

Step6: Find y-intercepts for all functions

• Function1: crosses y-axis at $(0,3)$, so $b=3$
• Function2: from table, when $x=0$, $y=-2$, so $b=-2$
• Function3: from $y=-3x-5$, $b=-5$
• Function4: given y-intercept $b=1$

Step7: Answer part (b)

Compare y-intercepts: $3>1>-2>-5$. Function1 has the greatest.

Answer:

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