Question

function a and function b are linear functions. function a: $y = 5x - 5$; function b: \

$$\begin{tabular}{|c|c|} \\hline $x$ & $y$ \\\\ \\hline -6 & -7 \\\\ \\hline -4 & -5 \\\\ \\hline -1 & -2 \\\\ \\hline \\end{tabular}$$

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 A

Function A is \( y = 5x - 5 \). In slope - intercept form \( y=mx + b \) (where \( m \) is the slope), the slope of Function A, \( m_A=5 \).

Step2: Calculate slope of Function B

The slope formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \).
Take two points from Function B's table, e.g., \((-6,-7)\) and \((-4,-5)\).
\( m_B=\frac{-5-(-7)}{-4 - (-6)}=\frac{-5 + 7}{-4 + 6}=\frac{2}{2}=1 \).
We can also check with other points, like \((-4,-5)\) and \((-1,-2)\): \( m_B=\frac{-2-(-5)}{-1-(-4)}=\frac{-2 + 5}{-1 + 4}=\frac{3}{3}=1 \).

Step3: Compare the slopes

Since \( 5>1 \), the slope of Function A (\( m_A = 5 \)) is greater than the slope of Function B (\( m_B=1 \)).

Answer:

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