QuestionWhich equation fits the points (-2,-1), (-1,1), (0,3), (1,5), (2,7)? Options: $y=x+2$ , $y=x+4$ , $y=2x+3$ , $y=3x+1$ .

Studdy Solution

STEP 1

Assumptions1. The table of values represents a linear function. . The relationship between $x$ and $y$ in the table can be represented by one of the given equations.

STEP 2

We will test each equation with the values from the table.Let's start with the first equation $y=x+2$ .

STEP 3

Substitute $x=-2$ into the equation $y=x+2$ .
$y=(-2)+2$

STEP 4

Calculate the value of $y$ .
$y=(-2)+2=0$

STEP 5

Compare the calculated value of $y$ with the value from the table. For $x=-2$ , the table gives $y=-1$ , but our calculation gives $y=0$ . Therefore, the equation $y=x+2$ does not represent the data in the table.

STEP 6

Let's test the second equation $y=x+4$ .

STEP 7

Substitute $x=-2$ into the equation $y=x+4$ .
$y=(-2)+4$

STEP 8

Calculate the value of $y$ .
$y=(-2)+4=2$

STEP 9

Compare the calculated value of $y$ with the value from the table. For $x=-2$ , the table gives $y=-$ , but our calculation gives $y=2$ . Therefore, the equation $y=x+4$ does not represent the data in the table.

STEP 10

Let's test the third equation $y=2x+3$ .

STEP 11

Substitute $x=-$ into the equation $y=x+3$ .
$y=(-)+3$

STEP 12

Calculate the value of $y$ .
$y=2(-2)+=-$

STEP 13

Compare the calculated value of $y$ with the value from the table. For $x=-2$ , the table gives $y=-$ , and our calculation also gives $y=-$ . So far, the equation $y=2x+3$ matches the data in the table.

STEP 14

To confirm, let's test another point from the table with the equation $y=2x+3$ . Substitute $x=0$ into the equation.
$y=2(0)+3$

STEP 15

Calculate the value of $y$ .
$y=2(0)+3=3$

STEP 16

Compare the calculated value of $y$ with the value from the table. For $x=0$ , the table gives $y=3$ , and our calculation also gives $y=3$ . Therefore, the equation $y=2x+3$ does represent the data in the table.
We don't need to test the fourth equation, because we've already found an equation that fits the data.
The equation that could represent the data in the table is $y=2x+3$ .

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QuestionWhich equation fits the points (-2,-1), (-1,1), (0,3), (1,5), (2,7)? Options: $y=x+2$ , $y=x+4$ , $y=2x+3$ , $y=3x+1$ .

Studdy Solution

STEP 1

Assumptions1. The table of values represents a linear function. . The relationship between $x$ and $y$ in the table can be represented by one of the given equations.

STEP 2

We will test each equation with the values from the table.Let's start with the first equation $y=x+2$ .

STEP 3

Substitute $x=-2$ into the equation $y=x+2$ .
$y=(-2)+2$

STEP 4

Calculate the value of $y$ .
$y=(-2)+2=0$

STEP 5

Compare the calculated value of $y$ with the value from the table. For $x=-2$ , the table gives $y=-1$ , but our calculation gives $y=0$ . Therefore, the equation $y=x+2$ does not represent the data in the table.

STEP 6

Let's test the second equation $y=x+4$ .

STEP 7

Substitute $x=-2$ into the equation $y=x+4$ .
$y=(-2)+4$

STEP 8

Calculate the value of $y$ .
$y=(-2)+4=2$

STEP 9

Compare the calculated value of $y$ with the value from the table. For $x=-2$ , the table gives $y=-$ , but our calculation gives $y=2$ . Therefore, the equation $y=x+4$ does not represent the data in the table.

STEP 10

Let's test the third equation $y=2x+3$ .

STEP 11

Substitute $x=-$ into the equation $y=x+3$ .
$y=(-)+3$

STEP 12

Calculate the value of $y$ .
$y=2(-2)+=-$

STEP 13

Compare the calculated value of $y$ with the value from the table. For $x=-2$ , the table gives $y=-$ , and our calculation also gives $y=-$ . So far, the equation $y=2x+3$ matches the data in the table.

STEP 14

To confirm, let's test another point from the table with the equation $y=2x+3$ . Substitute $x=0$ into the equation.
$y=2(0)+3$

STEP 15

Calculate the value of $y$ .
$y=2(0)+3=3$

STEP 16

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QuestionWhich equation fits the points (-2,-1), (-1,1), (0,3), (1,5), (2,7)? Options: y=x+2y=x+2y=x+2, y=x+4y=x+4y=x+4, y=2x+3y=2x+3y=2x+3, y=3x+1y=3x+1y=3x+1.

Studdy Solution

STEP 1

Assumptions1. The table of values represents a linear function. . The relationship between xxx and yyy in the table can be represented by one of the given equations.

STEP 2

We will test each equation with the values from the table.Let's start with the first equation y=x+2y=x+2y=x+2.

STEP 3

Substitute x=−2x=-2x=−2 into the equation y=x+2y=x+2y=x+2.y=(−2)+2y=(-2)+2y=(−2)+2

STEP 4

Calculate the value of yyy.y=(−2)+2=0y=(-2)+2=0y=(−2)+2=0

STEP 5

Compare the calculated value of yyy with the value from the table. For x=−2x=-2x=−2, the table gives y=−1y=-1y=−1, but our calculation gives y=0y=0y=0. Therefore, the equation y=x+2y=x+2y=x+2 does not represent the data in the table.

STEP 6

Let's test the second equation y=x+4y=x+4y=x+4.

STEP 7

Substitute x=−2x=-2x=−2 into the equation y=x+4y=x+4y=x+4.y=(−2)+4y=(-2)+4y=(−2)+4

STEP 8

Calculate the value of yyy.y=(−2)+4=2y=(-2)+4=2y=(−2)+4=2

STEP 9

Compare the calculated value of yyy with the value from the table. For x=−2x=-2x=−2, the table gives y=−y=-y=−, but our calculation gives y=2y=2y=2. Therefore, the equation y=x+4y=x+4y=x+4 does not represent the data in the table.

STEP 10

Let's test the third equation y=2x+3y=2x+3y=2x+3.

STEP 11

Substitute x=−x=-x=− into the equation y=x+3y=x+3y=x+3.y=(−)+3y=(-)+3y=(−)+3

STEP 12

Calculate the value of yyy.y=2(−2)+=−y=2(-2)+=-y=2(−2)+=−

STEP 13

Compare the calculated value of yyy with the value from the table. For x=−2x=-2x=−2, the table gives y=−y=-y=−, and our calculation also gives y=−y=-y=−. So far, the equation y=2x+3y=2x+3y=2x+3 matches the data in the table.

STEP 14

To confirm, let's test another point from the table with the equation y=2x+3y=2x+3y=2x+3. Substitute x=0x=0x=0 into the equation.y=2(0)+3y=2(0)+3y=2(0)+3

STEP 15

Calculate the value of yyy.y=2(0)+3=3y=2(0)+3=3y=2(0)+3=3

STEP 16

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QuestionWhich equation fits the points (-2,-1), (-1,1), (0,3), (1,5), (2,7)? Options: $y=x+2$ , $y=x+4$ , $y=2x+3$ , $y=3x+1$ .

Assumptions1. The table of values represents a linear function. . The relationship between $x$ and $y$ in the table can be represented by one of the given equations.

We will test each equation with the values from the table.Let's start with the first equation $y=x+2$ .

Substitute $x=-2$ into the equation $y=x+2$ .
$y=(-2)+2$

Calculate the value of $y$ .
$y=(-2)+2=0$

Compare the calculated value of $y$ with the value from the table. For $x=-2$ , the table gives $y=-1$ , but our calculation gives $y=0$ . Therefore, the equation $y=x+2$ does not represent the data in the table.

Let's test the second equation $y=x+4$ .

Substitute $x=-2$ into the equation $y=x+4$ .
$y=(-2)+4$

Calculate the value of $y$ .
$y=(-2)+4=2$

Compare the calculated value of $y$ with the value from the table. For $x=-2$ , the table gives $y=-$ , but our calculation gives $y=2$ . Therefore, the equation $y=x+4$ does not represent the data in the table.

Let's test the third equation $y=2x+3$ .

Substitute $x=-$ into the equation $y=x+3$ .
$y=(-)+3$

Calculate the value of $y$ .
$y=2(-2)+=-$

Compare the calculated value of $y$ with the value from the table. For $x=-2$ , the table gives $y=-$ , and our calculation also gives $y=-$ . So far, the equation $y=2x+3$ matches the data in the table.

To confirm, let's test another point from the table with the equation $y=2x+3$ . Substitute $x=0$ into the equation.
$y=2(0)+3$

Calculate the value of $y$ .
$y=2(0)+3=3$