Question

question 1-3
a function is shown.
$2x + 3y = 9$
which graph represents the function?
images of four graphs are shown, with some labeled points like (0,3), (4.5,0), etc.

Explanation:

Step1: Find x-intercept (y=0)

Substitute \( y = 0 \) into \( 2x + 3y = 9 \):
\( 2x + 3(0) = 9 \)
\( 2x = 9 \)
\( x = \frac{9}{2} = 4.5 \)
So x-intercept is \( (4.5, 0) \).

Step2: Find y-intercept (x=0)

Substitute \( x = 0 \) into \( 2x + 3y = 9 \):
\( 2(0) + 3y = 9 \)
\( 3y = 9 \)
\( y = 3 \)
So y-intercept is \( (0, 3) \).

Step3: Match intercepts to graphs

The line should pass through \( (4.5, 0) \) and \( (0, 3) \). Check the graphs: the first graph (top) has these intercepts.

Answer:

The graph with x-intercept (4.5, 0) and y-intercept (0, 3) (the top - most graph shown).