Question

function a and function b are linear functions.
function a

x	y
-10	-2
5	4
10	6

function b
graph of a line on a coordinate plane
which statement is true?
the y - value of function a when x = -5 is greater than the y - value of function b when x = -5.
the y - value of function a when x = -5 is less than the y - value of function b when x = -5.

Explanation:

Step1: Find slope of Function A

Use two points \((-10, -2)\) and \((5, 4)\). Slope \(m_A=\frac{4 - (-2)}{5 - (-10)}=\frac{6}{15}=\frac{2}{5}\).

Step2: Equation of Function A

Using point - slope form \(y - y_1 = m(x - x_1)\) with \((5,4)\): \(y - 4=\frac{2}{5}(x - 5)\), simplify to \(y=\frac{2}{5}x+2\).

Step3: Find y - value of A at \(x = - 5\)

Substitute \(x=-5\) into \(y=\frac{2}{5}x + 2\): \(y=\frac{2}{5}(-5)+2=-2 + 2=0\).

Step4: Find equation of Function B

From the graph, y - intercept \(b = 2\), slope \(m_B=\frac{2-0}{0 - (-10)}=\frac{2}{10}=\frac{1}{5}\). Equation: \(y=\frac{1}{5}x+2\).

Step5: Find y - value of B at \(x=-5\)

Substitute \(x = - 5\) into \(y=\frac{1}{5}x+2\): \(y=\frac{1}{5}(-5)+2=-1 + 2 = 1\).

Step6: Compare y - values

\(0<1\), so y - value of A at \(x=-5\) is less than y - value of B at \(x=-5\).

Answer:

The y - value of Function A when \(x=-5\) is less than the y - value of Function B when \(x=-5\).