Math / Geometry

QuestionGraph the equation $2x + y = 4$ .

Studdy Solution

STEP 1

What is this asking? We need to draw the line represented by the equation $2x + y = 4$ on a graph! Watch out! Make sure your points are plotted accurately and your line is straight.
A tiny mistake can lead to the wrong line!

STEP 2

1. Rewrite the equation
2. Find two points
3. Plot the points
4. Draw the line

STEP 3

Let's rewrite our equation $2x + y = 4$ in slope-intercept form ( $y = mx + b$ ), which makes graphing super easy!
Remember, $m$ is the slope and $b$ is the y-intercept.

STEP 4

To do this, we want to isolate $y$ .
We can subtract $2x$ from both sides of the equation: $2x + y - 2x = 4 - 2x$ .
This simplifies to $y = -2x + 4$ .
Now we're ready to rock!

STEP 5

Let's find two points that satisfy our equation $y = -2x + 4$ .
We can pick any value for $x$ and then solve for $y$ .

STEP 6

Let's choose $x = 0$ .
Substituting this into our equation gives us $y = -2 \cdot 0 + 4$ , which simplifies to $y = 4$ .
So our first point is $(0, 4)$ .

STEP 7

Now let's choose $x = 2$ .
Substituting this into our equation gives us $y = -2 \cdot 2 + 4$ , which simplifies to $y = -4 + 4 = 0$ .
So our second point is $(2, 0)$ .

STEP 8

Now, let's plot these two beautiful points, $(0, 4)$ and $(2, 0)$ , on the graph!
Remember, the first number in the pair is the $x$ -coordinate (how far we move left or right), and the second number is the $y$ -coordinate (how far we move up or down).

STEP 9

With our two points plotted, we can finally draw a straight line through them.
This line represents all the points that satisfy our equation $2x + y = 4$ !
Extend the line beyond the two points to show it continues infinitely.

STEP 10

The solution is the line drawn through the points $(0, 4)$ and $(2, 0)$ on the coordinate plane.

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QuestionGraph the equation $2x + y = 4$ .

Studdy Solution

STEP 1

What is this asking? We need to draw the line represented by the equation $2x + y = 4$ on a graph! Watch out! Make sure your points are plotted accurately and your line is straight.
A tiny mistake can lead to the wrong line!

STEP 2

1. Rewrite the equation
2. Find two points
3. Plot the points
4. Draw the line

STEP 3

Let's rewrite our equation $2x + y = 4$ in slope-intercept form ( $y = mx + b$ ), which makes graphing super easy!
Remember, $m$ is the slope and $b$ is the y-intercept.

STEP 4

To do this, we want to isolate $y$ .
We can subtract $2x$ from both sides of the equation: $2x + y - 2x = 4 - 2x$ .
This simplifies to $y = -2x + 4$ .
Now we're ready to rock!

STEP 5

Let's find two points that satisfy our equation $y = -2x + 4$ .
We can pick any value for $x$ and then solve for $y$ .

STEP 6

Let's choose $x = 0$ .
Substituting this into our equation gives us $y = -2 \cdot 0 + 4$ , which simplifies to $y = 4$ .
So our first point is $(0, 4)$ .

STEP 7

Now let's choose $x = 2$ .
Substituting this into our equation gives us $y = -2 \cdot 2 + 4$ , which simplifies to $y = -4 + 4 = 0$ .
So our second point is $(2, 0)$ .

STEP 8

Now, let's plot these two beautiful points, $(0, 4)$ and $(2, 0)$ , on the graph!
Remember, the first number in the pair is the $x$ -coordinate (how far we move left or right), and the second number is the $y$ -coordinate (how far we move up or down).

STEP 9

With our two points plotted, we can finally draw a straight line through them.
This line represents all the points that satisfy our equation $2x + y = 4$ !
Extend the line beyond the two points to show it continues infinitely.

STEP 10

The solution is the line drawn through the points $(0, 4)$ and $(2, 0)$ on the coordinate plane.

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QuestionGraph the equation 2x+y=42x + y = 42x+y=4.

Studdy Solution

STEP 1

What is this asking? We need to draw the line represented by the equation 2x+y=42x + y = 42x+y=4 on a graph! Watch out! Make sure your points are plotted accurately and your line is straight.A tiny mistake can lead to the wrong line!

STEP 2

1. Rewrite the equation2. Find two points3. Plot the points4. Draw the line

STEP 3

Let's **rewrite** our equation 2x+y=42x + y = 42x+y=4 in slope-intercept form (y=mx+by = mx + by=mx+b), which makes graphing super easy!Remember, mmm is the **slope** and bbb is the **y-intercept**.

STEP 4

To do this, we want to isolate yyy.We can **subtract** 2x2x2x from both sides of the equation: 2x+y−2x=4−2x2x + y - 2x = 4 - 2x2x+y−2x=4−2x.This simplifies to y=−2x+4y = -2x + 4y=−2x+4.Now we're ready to rock!

STEP 5

Let's find two points that satisfy our equation y=−2x+4y = -2x + 4y=−2x+4.We can pick any value for xxx and then solve for yyy.

STEP 6

Let's choose x=0x = 0x=0.Substituting this into our equation gives us y=−2⋅0+4y = -2 \cdot 0 + 4y=−2⋅0+4, which simplifies to y=4y = 4y=4.So our **first point** is (0,4)(0, 4)(0,4).

STEP 7

Now let's choose x=2x = 2x=2.Substituting this into our equation gives us y=−2⋅2+4y = -2 \cdot 2 + 4y=−2⋅2+4, which simplifies to y=−4+4=0y = -4 + 4 = 0y=−4+4=0.So our **second point** is (2,0)(2, 0)(2,0).

STEP 8

Now, let's **plot** these two beautiful points, (0,4)(0, 4)(0,4) and (2,0)(2, 0)(2,0), on the graph!Remember, the first number in the pair is the xxx-coordinate (how far we move left or right), and the second number is the yyy-coordinate (how far we move up or down).

STEP 9

With our two points plotted, we can finally **draw** a straight line through them.This line represents all the points that satisfy our equation 2x+y=42x + y = 42x+y=4!Extend the line beyond the two points to show it continues infinitely.

STEP 10

The solution is the line drawn through the points (0,4)(0, 4)(0,4) and (2,0)(2, 0)(2,0) on the coordinate plane.

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.

QuestionGraph the equation $2x + y = 4$ .

What is this asking? We need to draw the line represented by the equation $2x + y = 4$ on a graph! Watch out! Make sure your points are plotted accurately and your line is straight.
A tiny mistake can lead to the wrong line!

1. Rewrite the equation
2. Find two points
3. Plot the points
4. Draw the line

Let's rewrite our equation $2x + y = 4$ in slope-intercept form ( $y = mx + b$ ), which makes graphing super easy!
Remember, $m$ is the slope and $b$ is the y-intercept.

To do this, we want to isolate $y$ .
We can subtract $2x$ from both sides of the equation: $2x + y - 2x = 4 - 2x$ .
This simplifies to $y = -2x + 4$ .
Now we're ready to rock!

Let's find two points that satisfy our equation $y = -2x + 4$ .
We can pick any value for $x$ and then solve for $y$ .

Let's choose $x = 0$ .
Substituting this into our equation gives us $y = -2 \cdot 0 + 4$ , which simplifies to $y = 4$ .
So our first point is $(0, 4)$ .

Now let's choose $x = 2$ .
Substituting this into our equation gives us $y = -2 \cdot 2 + 4$ , which simplifies to $y = -4 + 4 = 0$ .
So our second point is $(2, 0)$ .

Now, let's plot these two beautiful points, $(0, 4)$ and $(2, 0)$ , on the graph!
Remember, the first number in the pair is the $x$ -coordinate (how far we move left or right), and the second number is the $y$ -coordinate (how far we move up or down).

With our two points plotted, we can finally draw a straight line through them.
This line represents all the points that satisfy our equation $2x + y = 4$ !
Extend the line beyond the two points to show it continues infinitely.

The solution is the line drawn through the points $(0, 4)$ and $(2, 0)$ on the coordinate plane.