Question

four different linear functions are represented below:
function 1
y = 3x + 7
function 2
the slope is -2 and the y-intercept is -6.
function 3

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

function 4
graph of a line on a coordinate plane
which function’s graph is the steepest?
○ function 4
○ function 2
○ function 3
○ function 1

Explanation:

Step1: Find slope of Function1

From $y=3x+7$, slope $m_1=3$

Step2: Find slope of Function2

Given slope $m_2=-2$

Step3: Calculate slope of Function3

Use $m=\frac{y_2-y_1}{x_2-x_1}$. Take $(x_1,y_1)=(-2,2)$, $(x_2,y_2)=(-1,3)$:
$m_3=\frac{3-2}{-1-(-2)}=\frac{1}{1}=1$

Step4: Calculate slope of Function4

Use graph points, e.g., $(0,1)$ and $(1,6)$:
$m_4=\frac{6-1}{1-0}=5$

Step5: Compare absolute slopes

$|m_1|=3$, $|m_2|=2$, $|m_3|=1$, $|m_4|=5$. Largest is 5.

Answer:

Function 4