Question

1. circle the line that represents ( 12 = 3x + 4y ). line a, line b, line c. show or explain how you know.

Explanation:

Answer:

To determine which line represents \( 12 = 3x + 4y \), we can find the \( x \)-intercept and \( y \)-intercept:

• For the \( x \)-intercept, set \( y = 0 \):

\( 12 = 3x + 4(0) \implies 3x = 12 \implies x = 4 \).
So the \( x \)-intercept is \( (4, 0) \).

• For the \( y \)-intercept, set \( x = 0 \):

\( 12 = 3(0) + 4y \implies 4y = 12 \implies y = 3 \).
So the \( y \)-intercept is \( (0, 3) \).

Now, check which line passes through \( (4, 0) \) and \( (0, 3) \). From the graph, Line \( b \) (or the appropriate labeled line) should intersect the \( x \)-axis at \( (4, 0) \) and the \( y \)-axis at \( (0, 3) \). Thus, the line representing \( 12 = 3x + 4y \) is the one with these intercepts (e.g., Line \( b \) if it matches the intercepts).