Math

Question Complete the table for the linear equation 4x3y=124x-3y=12 and graph the equation.

Studdy Solution

STEP 1

Assumptions1. The equation given is 4x3y=124x -3y =12 . We need to find the value of yy when x=0x =0

STEP 2

First, we need to isolate yy in the equation. We can do this by subtracting 4x4x from both sides of the equation.
y=4x+12-y = -4x +12

STEP 3

Now, divide both sides of the equation by 3-3 to solve for yy.
y=x3y = \frac{x}{3} -

STEP 4

Plug in the value of x=0x =0 into the equation to find the corresponding value of yy.
y=4034y = \frac{4 \cdot0}{3} -4

STEP 5

Calculate the value of yy.
y=04=4y =0 -4 = -4So, when x=0x =0, y=4y = -4.

STEP 6

Now, we can complete the table with the calculated value of yy.
\begin{tabular}{|c|c|} \hline x\mathbf{x} & y\mathbf{y} \\ \hline0 & 4-4 \\ \hline\end{tabular}

STEP 7

To graph the equation, we need at least two points. We already have one point (0,4)(0, -4). Let's find another point by choosing x=3x =3.
y=4334y = \frac{4 \cdot3}{3} -4

STEP 8

Calculate the value of yy.
y=44=0y =4 -4 =0So, when x=3x =3, y=0y =0. This gives us the second point (3,0)(3,0).

STEP 9

Now, we can plot these two points on the graph and draw a line through them to represent the equation 4x3y=124x -3y =12.
The graph will pass through the points (,4)(, -4) and (3,)(3,).

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