Math / Algebra

QuestionGraph the line with the equation $y = x - 4$ .

Studdy Solution

STEP 1

What is this asking? Draw the line represented by the equation $y = x - 4$ on a coordinate plane. Watch out! Make sure to correctly interpret the equation and plot the points accurately.
Don't mix up the $x$ and $y$ values!

STEP 2

1. Find the y-intercept.
2. Find the x-intercept.
3. Plot the line.

STEP 3

To find the y-intercept, we set $x = 0$ in our equation because the y-intercept is where the line crosses the y-axis, and the x-coordinate is always zero on the y-axis.

STEP 4

Substituting $x = 0$ into $y = x - 4$ , we get $y = 0 - 4$ .

STEP 5

So, $y = -4$ .
This means our y-intercept is at the point $(0, -4)$ .

STEP 6

To find the x-intercept, we set $y = 0$ because the x-intercept is where the line crosses the x-axis, and the y-coordinate is always zero on the x-axis.

STEP 7

Substituting $y = 0$ into $y = x - 4$ , we get $0 = x - 4$ .

STEP 8

Now, we want to isolate $x$ .
We can do this by adding 4 to both sides of the equation: $0 + 4 = x - 4 + 4$ .

STEP 9

This simplifies to $4 = x$ , or $x = 4$ .
So, our x-intercept is at the point $(4, 0)$ .

STEP 10

We have our two points: the y-intercept $(0, -4)$ and the x-intercept $(4, 0)$ .
Let's plot these points on the graph!

STEP 11

Now, draw a straight line through these two points, extending it in both directions.
This line represents all the points that satisfy the equation $y = x - 4$ .

STEP 12

The line passes through the points $(0, -4)$ and $(4, 0)$ on the coordinate plane.

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QuestionGraph the line with the equation $y = x - 4$ .

Studdy Solution

STEP 1

What is this asking? Draw the line represented by the equation $y = x - 4$ on a coordinate plane. Watch out! Make sure to correctly interpret the equation and plot the points accurately.
Don't mix up the $x$ and $y$ values!

STEP 2

1. Find the y-intercept.
2. Find the x-intercept.
3. Plot the line.

STEP 3

To find the y-intercept, we set $x = 0$ in our equation because the y-intercept is where the line crosses the y-axis, and the x-coordinate is always zero on the y-axis.

STEP 4

Substituting $x = 0$ into $y = x - 4$ , we get $y = 0 - 4$ .

STEP 5

So, $y = -4$ .
This means our y-intercept is at the point $(0, -4)$ .

STEP 6

To find the x-intercept, we set $y = 0$ because the x-intercept is where the line crosses the x-axis, and the y-coordinate is always zero on the x-axis.

STEP 7

Substituting $y = 0$ into $y = x - 4$ , we get $0 = x - 4$ .

STEP 8

Now, we want to isolate $x$ .
We can do this by adding 4 to both sides of the equation: $0 + 4 = x - 4 + 4$ .

STEP 9

This simplifies to $4 = x$ , or $x = 4$ .
So, our x-intercept is at the point $(4, 0)$ .

STEP 10

We have our two points: the y-intercept $(0, -4)$ and the x-intercept $(4, 0)$ .
Let's plot these points on the graph!

STEP 11

Now, draw a straight line through these two points, extending it in both directions.
This line represents all the points that satisfy the equation $y = x - 4$ .

STEP 12

The line passes through the points $(0, -4)$ and $(4, 0)$ on the coordinate plane.

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QuestionGraph the line with the equation y=x−4y = x - 4y=x−4.

Studdy Solution

STEP 1

What is this asking? Draw the line represented by the equation y=x−4y = x - 4y=x−4 on a coordinate plane. Watch out! Make sure to correctly interpret the equation and plot the points accurately.Don't mix up the xxx and yyy values!

STEP 2

1. Find the y-intercept.2. Find the x-intercept.3. Plot the line.

STEP 3

To **find the y-intercept**, we set x=0x = 0x=0 in our equation because the y-intercept is where the line crosses the y-axis, and the x-coordinate is always **zero** on the y-axis.

STEP 4

Substituting x=0x = 0x=0 into y=x−4y = x - 4y=x−4, we get y=0−4y = 0 - 4y=0−4.

STEP 5

So, y=−4y = -4y=−4.This means our **y-intercept** is at the point (0,−4)(0, -4)(0,−4).

STEP 6

To **find the x-intercept**, we set y=0y = 0y=0 because the x-intercept is where the line crosses the x-axis, and the y-coordinate is always **zero** on the x-axis.

STEP 7

Substituting y=0y = 0y=0 into y=x−4y = x - 4y=x−4, we get 0=x−40 = x - 40=x−4.

STEP 8

Now, we want to isolate xxx.We can do this by adding 4 to both sides of the equation: 0+4=x−4+40 + 4 = x - 4 + 40+4=x−4+4.

STEP 9

This simplifies to 4=x4 = x4=x, or x=4x = 4x=4.So, our **x-intercept** is at the point (4,0)(4, 0)(4,0).

STEP 10

We have our two points: the **y-intercept** (0,−4)(0, -4)(0,−4) and the **x-intercept** (4,0)(4, 0)(4,0).Let's plot these points on the graph!

STEP 11

Now, draw a straight line through these two points, extending it in both directions.This line represents all the points that satisfy the equation y=x−4y = x - 4y=x−4.

STEP 12

The line passes through the points (0,−4)(0, -4)(0,−4) and (4,0)(4, 0)(4,0) on the coordinate plane.

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QuestionGraph the line with the equation $y = x - 4$ .

What is this asking? Draw the line represented by the equation $y = x - 4$ on a coordinate plane. Watch out! Make sure to correctly interpret the equation and plot the points accurately.
Don't mix up the $x$ and $y$ values!

1. Find the y-intercept.
2. Find the x-intercept.
3. Plot the line.

To find the y-intercept, we set $x = 0$ in our equation because the y-intercept is where the line crosses the y-axis, and the x-coordinate is always zero on the y-axis.

Substituting $x = 0$ into $y = x - 4$ , we get $y = 0 - 4$ .

So, $y = -4$ .
This means our y-intercept is at the point $(0, -4)$ .

To find the x-intercept, we set $y = 0$ because the x-intercept is where the line crosses the x-axis, and the y-coordinate is always zero on the x-axis.

Substituting $y = 0$ into $y = x - 4$ , we get $0 = x - 4$ .

Now, we want to isolate $x$ .
We can do this by adding 4 to both sides of the equation: $0 + 4 = x - 4 + 4$ .

This simplifies to $4 = x$ , or $x = 4$ .
So, our x-intercept is at the point $(4, 0)$ .

We have our two points: the y-intercept $(0, -4)$ and the x-intercept $(4, 0)$ .
Let's plot these points on the graph!

Now, draw a straight line through these two points, extending it in both directions.
This line represents all the points that satisfy the equation $y = x - 4$ .

The line passes through the points $(0, -4)$ and $(4, 0)$ on the coordinate plane.