QuestionFor the equation $y=\frac{1}{3} x+3$ , find $y$ values for $x = 0, 3, -3, 6, -6$ .

Studdy Solution

STEP 1

Assumptions1. The equation is $y=\frac{1}{3} x+3$ . We need to find the $y$ values for $x$ values of0,3, -3,6, and -6

STEP 2

First, we need to find the $y$ value when $x=0$ . We can do this by substituting $x=0$ into the equation.
$y = \frac{1}{} \times0 +$

STEP 3

Calculate the $y$ value when $x=0$ .
$y =0 +3 =3$

STEP 4

Next, we need to find the $y$ value when $x=3$ . We can do this by substituting $x=3$ into the equation.
$y = \frac{1}{3} \times3 +3$

STEP 5

Calculate the $y$ value when $x=3$ .
$y =1 +3 =4$

STEP 6

Next, we need to find the $y$ value when $x=-3$ . We can do this by substituting $x=-3$ into the equation.
$y = \frac{1}{3} \times -3 +3$

STEP 7

Calculate the $y$ value when $x=-3$ .
$y = -1 +3 =2$

STEP 8

Next, we need to find the $y$ value when $x=6$ . We can do this by substituting $x=6$ into the equation.
$y = \frac{1}{3} \times6 +3$

STEP 9

Calculate the $y$ value when $x=6$ .
$y =2 +3 =5$

STEP 10

Finally, we need to find the $y$ value when $x=-6$ . We can do this by substituting $x=-6$ into the equation.
$y = \frac{}{3} \times -6 +3$

STEP 11

Calculate the $y$ value when $x=-6$ .
$y = - +3 =$ So, the filled table is\begin{tabular}{|l|l|} \hline $x$ & $y$ \\ \hline0 &3 \\ \hline3 &4 \\ \hline-3 & \\ \hline6 &5 \\ \hline-6 & \\ \hline\end{tabular}

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QuestionFor the equation $y=\frac{1}{3} x+3$ , find $y$ values for $x = 0, 3, -3, 6, -6$ .

Studdy Solution

STEP 1

Assumptions1. The equation is $y=\frac{1}{3} x+3$ . We need to find the $y$ values for $x$ values of0,3, -3,6, and -6

STEP 2

First, we need to find the $y$ value when $x=0$ . We can do this by substituting $x=0$ into the equation.
$y = \frac{1}{} \times0 +$

STEP 3

Calculate the $y$ value when $x=0$ .
$y =0 +3 =3$

STEP 4

Next, we need to find the $y$ value when $x=3$ . We can do this by substituting $x=3$ into the equation.
$y = \frac{1}{3} \times3 +3$

STEP 5

Calculate the $y$ value when $x=3$ .
$y =1 +3 =4$

STEP 6

Next, we need to find the $y$ value when $x=-3$ . We can do this by substituting $x=-3$ into the equation.
$y = \frac{1}{3} \times -3 +3$

STEP 7

Calculate the $y$ value when $x=-3$ .
$y = -1 +3 =2$

STEP 8

Next, we need to find the $y$ value when $x=6$ . We can do this by substituting $x=6$ into the equation.
$y = \frac{1}{3} \times6 +3$

STEP 9

Calculate the $y$ value when $x=6$ .
$y =2 +3 =5$

STEP 10

Finally, we need to find the $y$ value when $x=-6$ . We can do this by substituting $x=-6$ into the equation.
$y = \frac{}{3} \times -6 +3$

STEP 11

Calculate the $y$ value when $x=-6$ .
$y = - +3 =$ So, the filled table is\begin{tabular}{|l|l|} \hline $x$ & $y$ \\ \hline0 &3 \\ \hline3 &4 \\ \hline-3 & \\ \hline6 &5 \\ \hline-6 & \\ \hline\end{tabular}

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QuestionFor the equation y=13x+3y=\frac{1}{3} x+3y=31​x+3, find yyy values for x=0,3,−3,6,−6x = 0, 3, -3, 6, -6x=0,3,−3,6,−6.

Studdy Solution

STEP 1

Assumptions1. The equation is y=13x+3y=\frac{1}{3} x+3y=31​x+3 . We need to find the yyy values for xxx values of0,3, -3,6, and -6

STEP 2

First, we need to find the yyy value when x=0x=0x=0. We can do this by substituting x=0x=0x=0 into the equation.y=1×0+y = \frac{1}{} \times0 +y=1​×0+

STEP 3

Calculate the yyy value when x=0x=0x=0.y=0+3=3y =0 +3 =3y=0+3=3

STEP 4

Next, we need to find the yyy value when x=3x=3x=3. We can do this by substituting x=3x=3x=3 into the equation.y=13×3+3y = \frac{1}{3} \times3 +3y=31​×3+3

STEP 5

Calculate the yyy value when x=3x=3x=3.y=1+3=4y =1 +3 =4y=1+3=4

STEP 6

Next, we need to find the yyy value when x=−3x=-3x=−3. We can do this by substituting x=−3x=-3x=−3 into the equation.y=13×−3+3y = \frac{1}{3} \times -3 +3y=31​×−3+3

STEP 7

Calculate the yyy value when x=−3x=-3x=−3.y=−1+3=2y = -1 +3 =2y=−1+3=2

STEP 8

Next, we need to find the yyy value when x=6x=6x=6. We can do this by substituting x=6x=6x=6 into the equation.y=13×6+3y = \frac{1}{3} \times6 +3y=31​×6+3

STEP 9

Calculate the yyy value when x=6x=6x=6.y=2+3=5y =2 +3 =5y=2+3=5

STEP 10

Finally, we need to find the yyy value when x=−6x=-6x=−6. We can do this by substituting x=−6x=-6x=−6 into the equation.y=3×−6+3y = \frac{}{3} \times -6 +3y=3​×−6+3

STEP 11

Calculate the yyy value when x=−6x=-6x=−6.y=−+3=y = - +3 =y=−+3=So, the filled table is\begin{tabular}{|l|l|} \hlinexxx & yyy \\ \hline0 &3 \\ \hline3 &4 \\ \hline-3 & \\ \hline6 &5 \\ \hline-6 & \\ \hline\end{tabular}

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QuestionFor the equation $y=\frac{1}{3} x+3$ , find $y$ values for $x = 0, 3, -3, 6, -6$ .

Assumptions1. The equation is $y=\frac{1}{3} x+3$ . We need to find the $y$ values for $x$ values of0,3, -3,6, and -6

First, we need to find the $y$ value when $x=0$ . We can do this by substituting $x=0$ into the equation.
$y = \frac{1}{} \times0 +$

Calculate the $y$ value when $x=0$ .
$y =0 +3 =3$

Next, we need to find the $y$ value when $x=3$ . We can do this by substituting $x=3$ into the equation.
$y = \frac{1}{3} \times3 +3$

Calculate the $y$ value when $x=3$ .
$y =1 +3 =4$

Next, we need to find the $y$ value when $x=-3$ . We can do this by substituting $x=-3$ into the equation.
$y = \frac{1}{3} \times -3 +3$

Calculate the $y$ value when $x=-3$ .
$y = -1 +3 =2$

Next, we need to find the $y$ value when $x=6$ . We can do this by substituting $x=6$ into the equation.
$y = \frac{1}{3} \times6 +3$

Calculate the $y$ value when $x=6$ .
$y =2 +3 =5$

Finally, we need to find the $y$ value when $x=-6$ . We can do this by substituting $x=-6$ into the equation.
$y = \frac{}{3} \times -6 +3$

Calculate the $y$ value when $x=-6$ .
$y = - +3 =$ So, the filled table is\begin{tabular}{|l|l|} \hline $x$ & $y$ \\ \hline0 &3 \\ \hline3 &4 \\ \hline-3 & \\ \hline6 &5 \\ \hline-6 & \\ \hline\end{tabular}