QuestionGraph the line $-3y = x - 3$ by plotting at least two points on the axes. Use technology to assist you.

Studdy Solution

STEP 1

Assumptions1. We are given the equation of the line as $-3y = x -3$ . We need to plot this line on a graph3. We will use technology to assist in finding points and plotting the line

STEP 2

First, we need to rearrange the equation to the slope-intercept form, which is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.
$-y = x -$ Divide both sides by $-$ to solve for $y$ $y = -\frac{1}{}x +1$

STEP 3

Now, we can identify the slope and the y-intercept from the equation. The slope $m$ is $-\frac{1}{3}$ and the y-intercept $b$ is $1$ .

STEP 4

To plot the line, we need at least two points. One point is already given by the y-intercept, which is $(0,1)$ .

STEP 5

To find another point, we can choose an arbitrary value for $x$ and solve for $y$ . Let's choose $x =3$ .
Substitute $x =3$ into the equation $y = -\frac{1}{3}(3) +1$

STEP 6

Calculate the value of $y$ when $x =3$ .
$y = -1 +1 =0$ So, the second point is $(3,0)$ .

STEP 7

Now, we have two points, $(0,1)$ and $(3,0)$ . We can plot these points on the graph.

STEP 8

Draw a line through the points $(0,1)$ and $(3,0)$ . This line represents the equation $-3y = x -3$ .

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QuestionGraph the line $-3y = x - 3$ by plotting at least two points on the axes. Use technology to assist you.

Studdy Solution

STEP 1

Assumptions1. We are given the equation of the line as $-3y = x -3$ . We need to plot this line on a graph3. We will use technology to assist in finding points and plotting the line

STEP 2

First, we need to rearrange the equation to the slope-intercept form, which is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.
$-y = x -$ Divide both sides by $-$ to solve for $y$ $y = -\frac{1}{}x +1$

STEP 3

Now, we can identify the slope and the y-intercept from the equation. The slope $m$ is $-\frac{1}{3}$ and the y-intercept $b$ is $1$ .

STEP 4

To plot the line, we need at least two points. One point is already given by the y-intercept, which is $(0,1)$ .

STEP 5

To find another point, we can choose an arbitrary value for $x$ and solve for $y$ . Let's choose $x =3$ .
Substitute $x =3$ into the equation $y = -\frac{1}{3}(3) +1$

STEP 6

Calculate the value of $y$ when $x =3$ .
$y = -1 +1 =0$ So, the second point is $(3,0)$ .

STEP 7

Now, we have two points, $(0,1)$ and $(3,0)$ . We can plot these points on the graph.

STEP 8

Draw a line through the points $(0,1)$ and $(3,0)$ . This line represents the equation $-3y = x -3$ .

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QuestionGraph the line −3y=x−3-3y = x - 3−3y=x−3 by plotting at least two points on the axes. Use technology to assist you.

Studdy Solution

STEP 1

Assumptions1. We are given the equation of the line as −3y=x−3-3y = x -3−3y=x−3 . We need to plot this line on a graph3. We will use technology to assist in finding points and plotting the line

STEP 2

First, we need to rearrange the equation to the slope-intercept form, which is y=mx+by = mx + by=mx+b, where mmm is the slope and bbb is the y-intercept.−y=x−-y = x -−y=x−Divide both sides by −-− to solve for yyyy=−1x+1y = -\frac{1}{}x +1y=−1​x+1

STEP 3

Now, we can identify the slope and the y-intercept from the equation. The slope mmm is −13-\frac{1}{3}−31​ and the y-intercept bbb is 111.

STEP 4

To plot the line, we need at least two points. One point is already given by the y-intercept, which is (0,1)(0,1)(0,1).

STEP 5

To find another point, we can choose an arbitrary value for xxx and solve for yyy. Let's choose x=3x =3x=3.Substitute x=3x =3x=3 into the equationy=−13(3)+1y = -\frac{1}{3}(3) +1y=−31​(3)+1

STEP 6

Calculate the value of yyy when x=3x =3x=3.y=−1+1=0y = -1 +1 =0y=−1+1=0So, the second point is (3,0)(3,0)(3,0).

STEP 7

Now, we have two points, (0,1)(0,1)(0,1) and (3,0)(3,0)(3,0). We can plot these points on the graph.

STEP 8

Draw a line through the points (0,1)(0,1)(0,1) and (3,0)(3,0)(3,0). This line represents the equation −3y=x−3-3y = x -3−3y=x−3.

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QuestionGraph the line $-3y = x - 3$ by plotting at least two points on the axes. Use technology to assist you.

Assumptions1. We are given the equation of the line as $-3y = x -3$ . We need to plot this line on a graph3. We will use technology to assist in finding points and plotting the line

First, we need to rearrange the equation to the slope-intercept form, which is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.
$-y = x -$ Divide both sides by $-$ to solve for $y$ $y = -\frac{1}{}x +1$

Now, we can identify the slope and the y-intercept from the equation. The slope $m$ is $-\frac{1}{3}$ and the y-intercept $b$ is $1$ .

To plot the line, we need at least two points. One point is already given by the y-intercept, which is $(0,1)$ .

To find another point, we can choose an arbitrary value for $x$ and solve for $y$ . Let's choose $x =3$ .
Substitute $x =3$ into the equation $y = -\frac{1}{3}(3) +1$

Calculate the value of $y$ when $x =3$ .
$y = -1 +1 =0$ So, the second point is $(3,0)$ .

Now, we have two points, $(0,1)$ and $(3,0)$ . We can plot these points on the graph.

Draw a line through the points $(0,1)$ and $(3,0)$ . This line represents the equation $-3y = x -3$ .