Math / Geometry

Questione5f215874d2e4c3b1c6796601 and blue dots along the x -axis and y -axis to graph $-3 x+3 y=18$ .

Studdy Solution

STEP 1

What is this asking? We need to graph the line described by the equation $-3x + 3y = 18$ . Watch out! Make sure to simplify the equation before graphing to avoid unnecessary calculations!

STEP 2

1. Simplify the equation
2. Find the x-intercept
3. Find the y-intercept
4. Graph the line

STEP 3

Let's simplify our equation $-3x + 3y = 18$ .
We can make things easier by dividing both sides of the equation by 3.
Remember, as long as we do the same thing to both sides, the equation stays balanced!

STEP 4

Dividing both sides by $3$ gives us: $\frac{-3x}{3} + \frac{3y}{3} = \frac{18}{3}$ $-x + y = 6$

STEP 5

Now, let's isolate $y$ to get the equation into slope-intercept form ( $y = mx + b$ ).
We can do this by adding $x$ to both sides of the equation: $-x + y + x = 6 + x$ $y = x + 6$ Much nicer, right?
This simplified form will make finding our intercepts a breeze!

STEP 6

The x-intercept is where the line crosses the x-axis.
This happens when $y = 0$ .
Let's substitute $y = 0$ into our simplified equation: $0 = x + 6$

STEP 7

Now, subtract $6$ from both sides to solve for $x$ : $0 - 6 = x + 6 - 6$ $x = -6$ So, our x-intercept is $(-6, 0)$ !

STEP 8

The y-intercept is where the line crosses the y-axis, which happens when $x = 0$ .
Substitute $x = 0$ into our simplified equation: $y = 0 + 6$ $y = 6$ Awesome! Our y-intercept is $(0, 6)$ .

STEP 9

Now for the grand finale!
We have our x-intercept at $(-6, 0)$ and our y-intercept at $(0, 6)$ .
Plot these two points on your graph.

STEP 10

Draw a straight line through these two points, and voila!
You've graphed the line $-3x + 3y = 18$ !

STEP 11

The graph of the line is determined by the x-intercept at $(-6,0)$ and the y-intercept at $(0,6)$ .

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Questione5f215874d2e4c3b1c6796601 and blue dots along the x -axis and y -axis to graph $-3 x+3 y=18$ .

Studdy Solution

STEP 1

What is this asking? We need to graph the line described by the equation $-3x + 3y = 18$ . Watch out! Make sure to simplify the equation before graphing to avoid unnecessary calculations!

STEP 2

1. Simplify the equation
2. Find the x-intercept
3. Find the y-intercept
4. Graph the line

STEP 3

Let's simplify our equation $-3x + 3y = 18$ .
We can make things easier by dividing both sides of the equation by 3.
Remember, as long as we do the same thing to both sides, the equation stays balanced!

STEP 4

Dividing both sides by $3$ gives us: $\frac{-3x}{3} + \frac{3y}{3} = \frac{18}{3}$ $-x + y = 6$

STEP 5

Now, let's isolate $y$ to get the equation into slope-intercept form ( $y = mx + b$ ).
We can do this by adding $x$ to both sides of the equation: $-x + y + x = 6 + x$ $y = x + 6$ Much nicer, right?
This simplified form will make finding our intercepts a breeze!

STEP 6

The x-intercept is where the line crosses the x-axis.
This happens when $y = 0$ .
Let's substitute $y = 0$ into our simplified equation: $0 = x + 6$

STEP 7

Now, subtract $6$ from both sides to solve for $x$ : $0 - 6 = x + 6 - 6$ $x = -6$ So, our x-intercept is $(-6, 0)$ !

STEP 8

The y-intercept is where the line crosses the y-axis, which happens when $x = 0$ .
Substitute $x = 0$ into our simplified equation: $y = 0 + 6$ $y = 6$ Awesome! Our y-intercept is $(0, 6)$ .

STEP 9

Now for the grand finale!
We have our x-intercept at $(-6, 0)$ and our y-intercept at $(0, 6)$ .
Plot these two points on your graph.

STEP 10

Draw a straight line through these two points, and voila!
You've graphed the line $-3x + 3y = 18$ !

STEP 11

The graph of the line is determined by the x-intercept at $(-6,0)$ and the y-intercept at $(0,6)$ .

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Questione5f215874d2e4c3b1c6796601 and blue dots along the x -axis and y -axis to graph −3x+3y=18-3 x+3 y=18−3x+3y=18.

Studdy Solution

STEP 1

What is this asking? We need to graph the line described by the equation −3x+3y=18-3x + 3y = 18−3x+3y=18. Watch out! Make sure to simplify the equation before graphing to avoid unnecessary calculations!

STEP 2

1. Simplify the equation2. Find the x-intercept3. Find the y-intercept4. Graph the line

STEP 3

Let's **simplify** our equation −3x+3y=18-3x + 3y = 18−3x+3y=18.We can make things easier by dividing both sides of the equation by **3**.Remember, as long as we do the same thing to both sides, the equation stays balanced!

STEP 4

Dividing both sides by 333 gives us: −3x3+3y3=183 \frac{-3x}{3} + \frac{3y}{3} = \frac{18}{3} 3−3x​+33y​=318​ −x+y=6 -x + y = 6 −x+y=6

STEP 5

STEP 6

The **x-intercept** is where the line crosses the x-axis.This happens when y=0y = 0y=0.Let's substitute y=0y = 0y=0 into our simplified equation: 0=x+6 0 = x + 6 0=x+6

STEP 7

Now, subtract 666 from both sides to solve for xxx: 0−6=x+6−6 0 - 6 = x + 6 - 6 0−6=x+6−6 x=−6 x = -6 x=−6So, our **x-intercept** is (−6,0)(-6, 0)(−6,0)!

STEP 8

The **y-intercept** is where the line crosses the y-axis, which happens when x=0x = 0x=0.Substitute x=0x = 0x=0 into our simplified equation: y=0+6 y = 0 + 6 y=0+6 y=6 y = 6 y=6Awesome! Our **y-intercept** is (0,6)(0, 6)(0,6).

STEP 9

Now for the grand finale!We have our **x-intercept** at (−6,0)(-6, 0)(−6,0) and our **y-intercept** at (0,6)(0, 6)(0,6).Plot these two points on your graph.

STEP 10

Draw a straight line through these two points, and voila!You've graphed the line −3x+3y=18-3x + 3y = 18−3x+3y=18!

STEP 11

The graph of the line is determined by the x-intercept at (−6,0)(-6,0)(−6,0) and the y-intercept at (0,6)(0,6)(0,6).

Get Studdy

Studdy solves anything!

Start learning now

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

Questione5f215874d2e4c3b1c6796601 and blue dots along the x -axis and y -axis to graph $-3 x+3 y=18$ .

What is this asking? We need to graph the line described by the equation $-3x + 3y = 18$ . Watch out! Make sure to simplify the equation before graphing to avoid unnecessary calculations!

1. Simplify the equation
2. Find the x-intercept
3. Find the y-intercept
4. Graph the line

Let's simplify our equation $-3x + 3y = 18$ .
We can make things easier by dividing both sides of the equation by 3.
Remember, as long as we do the same thing to both sides, the equation stays balanced!

Dividing both sides by $3$ gives us: $\frac{-3x}{3} + \frac{3y}{3} = \frac{18}{3}$ $-x + y = 6$

The x-intercept is where the line crosses the x-axis.
This happens when $y = 0$ .
Let's substitute $y = 0$ into our simplified equation: $0 = x + 6$

Now, subtract $6$ from both sides to solve for $x$ : $0 - 6 = x + 6 - 6$ $x = -6$ So, our x-intercept is $(-6, 0)$ !

The y-intercept is where the line crosses the y-axis, which happens when $x = 0$ .
Substitute $x = 0$ into our simplified equation: $y = 0 + 6$ $y = 6$ Awesome! Our y-intercept is $(0, 6)$ .

Now for the grand finale!
We have our x-intercept at $(-6, 0)$ and our y-intercept at $(0, 6)$ .
Plot these two points on your graph.

Draw a straight line through these two points, and voila!
You've graphed the line $-3x + 3y = 18$ !

The graph of the line is determined by the x-intercept at $(-6,0)$ and the y-intercept at $(0,6)$ .