Question

identify the graph of the following equation.
3x + 4y = 12

choose the correct graph below.
a.

b.

c.

d.

Explanation:

Step1: Find x-intercept

Set \( y = 0 \) in \( 3x + 4y = 12 \).
\( 3x + 4(0) = 12 \)
\( 3x = 12 \)
\( x = 4 \). So x-intercept is \( (4, 0) \).

Step2: Find y-intercept

Set \( x = 0 \) in \( 3x + 4y = 12 \).
\( 3(0) + 4y = 12 \)
\( 4y = 12 \)
\( y = 3 \). So y-intercept is \( (0, 3) \).

Step3: Analyze the line

The equation \( 3x + 4y = 12 \) can be rewritten as \( y = -\frac{3}{4}x + 3 \), which has a negative slope. A line with negative slope decreases from left to right. The intercepts are \( (4, 0) \) and \( (0, 3) \), so we look for the graph with these intercepts and a negative slope. Among the options, option C should match (since it has a negative slope and passes through \( (4, 0) \) and \( (0, 3) \) approximately, based on the intercepts and slope analysis).

Answer:

C