Question

question 14 of 16, step 1 of 1
use your knowledge of x - and y - intercepts to choose the correct graph of the equation.
4x + 6y = 12.
answer
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enter the appropriate letter for the graph.

Explanation:

Step1: Find x-intercept (y=0)

Substitute \( y = 0 \) into \( 4x + 6y = 12 \):
\( 4x + 6(0) = 12 \)
\( 4x = 12 \)
\( x = \frac{12}{4} = 3 \)
So x-intercept is \( (3, 0) \).

Step2: Find y-intercept (x=0)

Substitute \( x = 0 \) into \( 4x + 6y = 12 \):
\( 4(0) + 6y = 12 \)
\( 6y = 12 \)
\( y = \frac{12}{6} = 2 \)
So y-intercept is \( (0, 2) \).

Step3: Match intercepts to graphs

The line should pass through \( (3, 0) \) (on x-axis) and \( (0, 2) \) (on y-axis). Graph c has a positive y-intercept and crosses the x-axis at a positive x-value (near 3) and slopes downward (consistent with \( 4x + 6y = 12 \) rearranged as \( y = -\frac{2}{3}x + 2 \), negative slope).

Answer:

c