Question

function a and function b are linear functions. function a \

$$\begin{tabular}{|c|c|} \\hline x & y \\\\ \\hline -6 & -25 \\\\ \\hline -3 & -10 \\\\ \\hline 2 & 15 \\\\ \\hline \\end{tabular}$$

function b $y = 2x - 5$ which statement is true? the slope of function a is greater than the slope of function b. the slope of function a is less than the slope of function b.

Explanation:

Step1: Find slope of Function B

Function B is in slope-intercept form $y=mx+b$, where $m$ is slope. So slope of B is $m_B=2$.

Step2: Calculate slope of Function A

Use slope formula $m=\frac{y_2-y_1}{x_2-x_1}$ with points $(-6,-25)$ and $(-3,-10)$:
$\frac{-10 - (-25)}{-3 - (-6)}=\frac{15}{3}=5$
Verify with another pair $(-3,-10)$ and $(2,15)$:
$\frac{15 - (-10)}{2 - (-3)}=\frac{25}{5}=5$. So slope of A is $m_A=5$.

Step3: Compare the two slopes

$5 > 2$, so $m_A > m_B$.

Answer:

The slope of Function A is greater than the slope of Function B.