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QuestionEvaluate the equation y=−3x+2y=-3x+2 for x=−4,−2,−1,4x=-4, -2, -1, 4. What are the corresponding yy values?

Studdy Solution

STEP 1

Assumptions1. We have a linear equation given by y=−3x+y=-3x+. . We are given four values of xx and asked to find the corresponding values of yy.

STEP 2

The general form of a linear equation is y=mx+cy=mx+c, where mm is the slope and cc is the y-intercept. In our case, m=−m=- and c=2c=2.

STEP 3

To find the value of yy for a given xx, we substitute the value of xx into the equation and solve for yy.

STEP 4

Let's find the value of yy when x=−4x=-4. Substitute x=−4x=-4 into the equation.
y=−3(−4)+2y=-3(-4)+2

STEP 5

Calculate the value of yy.
y=12+2=14y=12+2=14

STEP 6

So, when x=−4x=-4, y=14y=14.

STEP 7

Next, let's find the value of yy when x=−2x=-2. Substitute x=−2x=-2 into the equation.
y=−3(−2)+2y=-3(-2)+2

STEP 8

Calculate the value of yy.
y=6+2=8y=6+2=8

STEP 9

So, when x=−2x=-2, y=8y=8.

STEP 10

Next, let's find the value of yy when x=−x=-. Substitute x=−x=- into the equation.
y=−3(−)+2y=-3(-)+2

STEP 11

Calculate the value of yy.
y=3+=5y=3+=5

STEP 12

So, when x=−x=-, y=5y=5.

STEP 13

Finally, let's find the value of yy when x=x=. Substitute x=x= into the equation.
y=−3()+2y=-3()+2

STEP 14

Calculate the value of yy.
y=−12+2=−10y=-12+2=-10

STEP 15

So, when x=4x=4, y=−10y=-10.
The completed table is\begin{tabular}{||l|l||} \hlinexx & yy \\ \hline \hline-4 &14 \\ \hline \hline-2 &8 \\ \hline- &5 \\ \hline4 & -10 \\ \hline\end{tabular}

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