Question

function a and function b are linear functions.
function a
(graph of a line on a coordinate plane with x-axis from -10 to 10 and y-axis from -10 to 10. the line passes through (-4, 0) and (0, 4))
function b
$y = 3x - 2$
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 y for Function A at x=2

From the graph of Function A (linear), when \( x = 2 \), we can see the point \((2, 6)\) (by counting grid or slope-intercept). So \( y_A = 6 \).

Step2: Find y for Function B at x=2

Function B: \( y = 3x - 2 \). Substitute \( x = 2 \): \( y_B = 3(2) - 2 = 6 - 2 = 4 \).

Step3: Compare y-values

\( y_A = 6 \), \( y_B = 4 \). So \( y_A > y_B \) at \( x = 2 \).

Answer:

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