QuestionDetermine $x$ , $y$ , $m$ (slope), and $b$ (y-intercept) for the equation $y=2x+2$ .

Studdy Solution

STEP 1

Assumptions1. The given equation is in the form of a linear equation, $y=mx+b$ , where $m$ is the slope and $b$ is the y-intercept. . The equation is $y=x+$ .

STEP 2

In the given equation, the coefficient of $x$ is the slope ( $m$ ) of the line. So, we can directly equate the coefficient of $x$ to $m$ .
$m =2$

STEP 3

In the given equation, the constant term is the y-intercept ( $b$ ) of the line. So, we can directly equate the constant term to $b$ .
$b =2$

STEP 4

The values of $x$ and $y$ are not given directly in the problem. However, we can find the possible values of $x$ and $y$ by substituting any value for $x$ in the equation and solving for $y$ .For example, let's substitute $x=1$ in the equation.
$y =2(1) +2$

STEP 5

Calculate the value of $y$ .
$y =2(1) +2 =4$ So, when $x=1$ , $y=4$ .

STEP 6

Similarly, we can find another pair of $x$ and $y$ by substituting another value for $x$ in the equation.For example, let's substitute $x=2$ in the equation.
$y =2(2) +2$

STEP 7

Calculate the value of $y$ .
$y =2(2) +2 =6$ So, when $x=2$ , $y=6$ .
In conclusion, the values of $m$ and $b$ are2, and the values of $x$ and $y$ can be any pair of values that satisfy the equation $y=2x+2$ . Two such pairs of values are $(1,4)$ and $(2,6)$ .

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QuestionDetermine $x$ , $y$ , $m$ (slope), and $b$ (y-intercept) for the equation $y=2x+2$ .

Studdy Solution

STEP 1

Assumptions1. The given equation is in the form of a linear equation, $y=mx+b$ , where $m$ is the slope and $b$ is the y-intercept. . The equation is $y=x+$ .

STEP 2

In the given equation, the coefficient of $x$ is the slope ( $m$ ) of the line. So, we can directly equate the coefficient of $x$ to $m$ .
$m =2$

STEP 3

In the given equation, the constant term is the y-intercept ( $b$ ) of the line. So, we can directly equate the constant term to $b$ .
$b =2$

STEP 4

The values of $x$ and $y$ are not given directly in the problem. However, we can find the possible values of $x$ and $y$ by substituting any value for $x$ in the equation and solving for $y$ .For example, let's substitute $x=1$ in the equation.
$y =2(1) +2$

STEP 5

Calculate the value of $y$ .
$y =2(1) +2 =4$ So, when $x=1$ , $y=4$ .

STEP 6

Similarly, we can find another pair of $x$ and $y$ by substituting another value for $x$ in the equation.For example, let's substitute $x=2$ in the equation.
$y =2(2) +2$

STEP 7

Calculate the value of $y$ .
$y =2(2) +2 =6$ So, when $x=2$ , $y=6$ .
In conclusion, the values of $m$ and $b$ are2, and the values of $x$ and $y$ can be any pair of values that satisfy the equation $y=2x+2$ . Two such pairs of values are $(1,4)$ and $(2,6)$ .

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QuestionDetermine xxx, yyy, mmm (slope), and bbb (y-intercept) for the equation y=2x+2y=2x+2y=2x+2.

Studdy Solution

STEP 1

Assumptions1. The given equation is in the form of a linear equation, y=mx+by=mx+by=mx+b, where mmm is the slope and bbb is the y-intercept. . The equation is y=x+y=x+y=x+.

STEP 2

In the given equation, the coefficient of xxx is the slope (mmm) of the line. So, we can directly equate the coefficient of xxx to mmm.m=2m =2m=2

STEP 3

In the given equation, the constant term is the y-intercept (bbb) of the line. So, we can directly equate the constant term to bbb.b=2b =2b=2

STEP 4

The values of xxx and yyy are not given directly in the problem. However, we can find the possible values of xxx and yyy by substituting any value for xxx in the equation and solving for yyy.For example, let's substitute x=1x=1x=1 in the equation.y=2(1)+2y =2(1) +2y=2(1)+2

STEP 5

Calculate the value of yyy.y=2(1)+2=4y =2(1) +2 =4y=2(1)+2=4So, when x=1x=1x=1, y=4y=4y=4.

STEP 6

Similarly, we can find another pair of xxx and yyy by substituting another value for xxx in the equation.For example, let's substitute x=2x=2x=2 in the equation.y=2(2)+2y =2(2) +2y=2(2)+2

STEP 7

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QuestionDetermine $x$ , $y$ , $m$ (slope), and $b$ (y-intercept) for the equation $y=2x+2$ .

Assumptions1. The given equation is in the form of a linear equation, $y=mx+b$ , where $m$ is the slope and $b$ is the y-intercept. . The equation is $y=x+$ .

In the given equation, the coefficient of $x$ is the slope ( $m$ ) of the line. So, we can directly equate the coefficient of $x$ to $m$ .
$m =2$

In the given equation, the constant term is the y-intercept ( $b$ ) of the line. So, we can directly equate the constant term to $b$ .
$b =2$

The values of $x$ and $y$ are not given directly in the problem. However, we can find the possible values of $x$ and $y$ by substituting any value for $x$ in the equation and solving for $y$ .For example, let's substitute $x=1$ in the equation.
$y =2(1) +2$

Calculate the value of $y$ .
$y =2(1) +2 =4$ So, when $x=1$ , $y=4$ .

Similarly, we can find another pair of $x$ and $y$ by substituting another value for $x$ in the equation.For example, let's substitute $x=2$ in the equation.
$y =2(2) +2$