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Graphing Linear Functions in Standard Form

Graphing Linear Functions in Standard Form 1.2 - Solution

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Each graph has a different set of x-x\text{-} and y-y\text{-}intercepts. By finding these, we can identify which graph belongs to which equation.

x-x\text{-}intercept

The x-x\text{-}intercept occurs when y=0.y=0. By substituting 00 for yy into our equation and solving for x,x, we can find the x-x\text{-}intercept.
4x+3y=124x+3y=12
4x+30=124x+3\cdot{\color{#0000FF}{0}}=12
Solve for xx
4x+0=124x+0=12
4x=124x=12
x=3x=3
The x-x\text{-}intercept is at the point (3,0).(3,0).

y-y\text{-}intercept

To find the y-y\text{-}intercept, we substitute 00 for xx and solve for y.y.
4x+3y=124x+3y=12
40+3y=124\cdot{\color{#0000FF}{0}}+3y=12
Solve for yy
0+3y=120+3y=12
3y=123y=12
y=4y=4
The y-y\text{-}intercept is at the point (0,4).(0,4).

Graph

Now that we know the intercepts, we can draw the graph of this equation.

This graph corresponds to option A.A.