Solved on Jan 23, 2024

Find the equation for a line with the equation $y=x$ .

STEP 1

Assumptions
1. We are given the equation of a line in the form $y = x$ .
2. We need to express this equation in the standard form of a linear equation, which is $Ax + By = C$ , where $A$ , $B$ , and $C$ are constants.

STEP 2

The given equation is already in a form that represents a line. The slope-intercept form of a line is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

STEP 3

In the given equation $y = x$ , the slope $m$ is 1 (since $x$ is the same as $1x$ ) and the y-intercept $b$ is 0 (since there is no constant added to $x$ ).

STEP 4

To write the equation in standard form $Ax + By = C$ , we can simply rewrite the given equation by moving $x$ to the left side of the equation.

STEP 5

Subtract $x$ from both sides of the equation to move it to the left side.
$y - x = 0$

STEP 6

Now, the equation $y - x = 0$ is in the standard form $Ax + By = C$ , where $A = -1$ , $B = 1$ , and $C = 0$ .
The equation for the line is $-x + y = 0$ .

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Find the equation for a line with the equation $y=x$ .

STEP 1

Assumptions
1. We are given the equation of a line in the form $y = x$ .
2. We need to express this equation in the standard form of a linear equation, which is $Ax + By = C$ , where $A$ , $B$ , and $C$ are constants.

STEP 2

The given equation is already in a form that represents a line. The slope-intercept form of a line is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

STEP 3

In the given equation $y = x$ , the slope $m$ is 1 (since $x$ is the same as $1x$ ) and the y-intercept $b$ is 0 (since there is no constant added to $x$ ).

STEP 4

To write the equation in standard form $Ax + By = C$ , we can simply rewrite the given equation by moving $x$ to the left side of the equation.

STEP 5

Subtract $x$ from both sides of the equation to move it to the left side.
$y - x = 0$

STEP 6

Now, the equation $y - x = 0$ is in the standard form $Ax + By = C$ , where $A = -1$ , $B = 1$ , and $C = 0$ .
The equation for the line is $-x + y = 0$ .

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Find the equation for a line with the equation y=xy=xy=x.

STEP 1

Assumptions1. We are given the equation of a line in the form y=xy = xy=x.2. We need to express this equation in the standard form of a linear equation, which is Ax+By=CAx + By = CAx+By=C, where AAA, BBB, and CCC are constants.

STEP 2

The given equation is already in a form that represents a line. The slope-intercept form of a line is y=mx+by = mx + by=mx+b, where mmm is the slope and bbb is the y-intercept.

STEP 3

In the given equation y=xy = xy=x, the slope mmm is 1 (since xxx is the same as 1x1x1x) and the y-intercept bbb is 0 (since there is no constant added to xxx).

STEP 4

To write the equation in standard form Ax+By=CAx + By = CAx+By=C, we can simply rewrite the given equation by moving xxx to the left side of the equation.

STEP 5

Subtract xxx from both sides of the equation to move it to the left side.y−x=0y - x = 0y−x=0

STEP 6

Now, the equation y−x=0y - x = 0y−x=0 is in the standard form Ax+By=CAx + By = CAx+By=C, where A=−1A = -1A=−1, B=1B = 1B=1, and C=0C = 0C=0.The equation for the line is −x+y=0-x + y = 0−x+y=0.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find the equation for a line with the equation $y=x$ .

Assumptions
1. We are given the equation of a line in the form $y = x$ .
2. We need to express this equation in the standard form of a linear equation, which is $Ax + By = C$ , where $A$ , $B$ , and $C$ are constants.

The given equation is already in a form that represents a line. The slope-intercept form of a line is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

In the given equation $y = x$ , the slope $m$ is 1 (since $x$ is the same as $1x$ ) and the y-intercept $b$ is 0 (since there is no constant added to $x$ ).

To write the equation in standard form $Ax + By = C$ , we can simply rewrite the given equation by moving $x$ to the left side of the equation.

Subtract $x$ from both sides of the equation to move it to the left side.
$y - x = 0$

Now, the equation $y - x = 0$ is in the standard form $Ax + By = C$ , where $A = -1$ , $B = 1$ , and $C = 0$ .
The equation for the line is $-x + y = 0$ .