Question

function a and function b are linear functions.
function a

x	y
-7	-23
-4	-11
3	17

function b
$y = \frac{1}{2}x - 5$
which statement is true?
the y-value of function a when $x = -2$ is greater than the y-value of function b when $x = -2$.
the y-value of function a when $x = -2$ is less than the y-value of function b when $x = -2$.

Explanation:

Step1: Find the slope of Function A

Use two points from Function A's table, say \((-7, -23)\) and \((-4, -11)\). The slope \(m\) is calculated as \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{-11 - (-23)}{-4 - (-7)}=\frac{12}{3} = 4\).

Step2: Find the equation of Function A

Using point - slope form \(y - y_1=m(x - x_1)\) with point \((-4, -11)\) and \(m = 4\).
\(y-(-11)=4(x - (-4))\)
\(y + 11=4(x + 4)\)
\(y+11 = 4x+16\)
\(y=4x + 5\)

Step3: Find the y - value of Function A when \(x=-2\)

Substitute \(x = - 2\) into \(y = 4x+5\).
\(y=4\times(-2)+5=-8 + 5=-3\)

Step4: Find the y - value of Function B when \(x=-2\)

Function B's equation is \(y=\frac{1}{2}x-5\). Substitute \(x=-2\) into it.
\(y=\frac{1}{2}\times(-2)-5=-1 - 5=-6\)

Step5: Compare the two y - values

We have \(y_A=-3\) and \(y_B = - 6\). Since \(-3>-6\), the y - value of Function A when \(x = - 2\) is greater than the y - value of Function B when \(x=-2\).

Answer:

The y - value of Function A when \(x=-2\) is greater than the y - value of Function B when \(x = - 2\).