Math / Algebra

QuestionWhat are the slope, $x$ -intercept, and $y$ -intercept of the line represented by the equation? $4 x+4 y=8$ slope $=-1, x$ -intercept $=4, y$ -intercept $=4$ 4 slope $=4, x$ -intercept $=2, y$ -intercept $=-2$ slope $=4, x$ -intercept $=-1, y$ -intercept $=2$ slope $=-1, x$ -intercept $=2, y$ -intercept $=2$

Studdy Solution

STEP 1

What is this asking? We need to find the slope, x-intercept, and y-intercept of a line given its equation. Watch out! Don't mix up the x and y intercepts!
Also, remember the slope-intercept form requires us to isolate $y$ .

STEP 2

1. Rewrite in slope-intercept form.
2. Identify the slope.
3. Calculate the x-intercept.
4. Calculate the y-intercept.

STEP 3

We start with $4x + 4y = 8$ .
To get to slope-intercept form, we want to isolate $y$ .
Let's subtract $4x$ from both sides of the equation: $4x + 4y - 4x = 8 - 4x$ $4y = 8 - 4x$

STEP 4

Now, we divide both sides by $4$ to completely isolate $y$ : $\frac{4y}{4} = \frac{8 - 4x}{4}$ $y = \frac{8}{4} - \frac{4x}{4}$ $y = 2 - x$

STEP 5

Finally, we rewrite the equation in the standard slope-intercept form $y = mx + b$ : $y = -x + 2$

STEP 6

In the slope-intercept form $y = mx + b$ , $m$ represents the slope.
In our equation $y = -x + 2$ , the coefficient of $x$ is $-1$ , so our slope is $m = -1$ .
Boom!

STEP 7

The x-intercept is where the line crosses the x-axis, meaning $y = 0$ .
Let's substitute $y = 0$ into our equation: $0 = -x + 2$

STEP 8

Now, we solve for $x$ .
We can add $x$ to both sides: $x = 2$ So, the x-intercept is $2$ .

STEP 9

In the slope-intercept form $y = mx + b$ , $b$ represents the y-intercept.
In our equation $y = -x + 2$ , $b = 2$ .
So, the y-intercept is $2$ .
Awesome!

STEP 10

The slope is $-1$ , the x-intercept is $2$ , and the y-intercept is $2$ .

Was this helpful?

Studdy Solution

STEP 1

What is this asking? We need to find the slope, x-intercept, and y-intercept of a line given its equation. Watch out! Don't mix up the x and y intercepts!
Also, remember the slope-intercept form requires us to isolate $y$ .

STEP 2

1. Rewrite in slope-intercept form.
2. Identify the slope.
3. Calculate the x-intercept.
4. Calculate the y-intercept.

STEP 3

We start with $4x + 4y = 8$ .
To get to slope-intercept form, we want to isolate $y$ .
Let's subtract $4x$ from both sides of the equation: $4x + 4y - 4x = 8 - 4x$ $4y = 8 - 4x$

STEP 4

Now, we divide both sides by $4$ to completely isolate $y$ : $\frac{4y}{4} = \frac{8 - 4x}{4}$ $y = \frac{8}{4} - \frac{4x}{4}$ $y = 2 - x$

STEP 5

Finally, we rewrite the equation in the standard slope-intercept form $y = mx + b$ : $y = -x + 2$

STEP 6

In the slope-intercept form $y = mx + b$ , $m$ represents the slope.
In our equation $y = -x + 2$ , the coefficient of $x$ is $-1$ , so our slope is $m = -1$ .
Boom!

STEP 7

The x-intercept is where the line crosses the x-axis, meaning $y = 0$ .
Let's substitute $y = 0$ into our equation: $0 = -x + 2$

STEP 8

Now, we solve for $x$ .
We can add $x$ to both sides: $x = 2$ So, the x-intercept is $2$ .

STEP 9

In the slope-intercept form $y = mx + b$ , $b$ represents the y-intercept.
In our equation $y = -x + 2$ , $b = 2$ .
So, the y-intercept is $2$ .
Awesome!

STEP 10

The slope is $-1$ , the x-intercept is $2$ , and the y-intercept is $2$ .

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.

Studdy Solution

STEP 1

What is this asking? We need to find the slope, *x*-intercept, and *y*-intercept of a line given its equation. Watch out! Don't mix up the *x* and *y* intercepts!Also, remember the slope-intercept form requires us to isolate yyy.

STEP 2

1. Rewrite in slope-intercept form.2. Identify the slope.3. Calculate the *x*-intercept.4. Calculate the *y*-intercept.

STEP 3

We **start** with 4x+4y=84x + 4y = 84x+4y=8.To get to slope-intercept form, we want to isolate yyy.Let's **subtract** 4x4x4x from both sides of the equation: 4x+4y−4x=8−4x4x + 4y - 4x = 8 - 4x4x+4y−4x=8−4x 4y=8−4x4y = 8 - 4x4y=8−4x

STEP 4

Now, we **divide** both sides by 444 to completely isolate yyy: 4y4=8−4x4\frac{4y}{4} = \frac{8 - 4x}{4}44y​=48−4x​ y=84−4x4y = \frac{8}{4} - \frac{4x}{4}y=48​−44x​y=2−xy = 2 - xy=2−x

STEP 5

Finally, we **rewrite** the equation in the standard slope-intercept form y=mx+by = mx + by=mx+b: y=−x+2y = -x + 2y=−x+2

STEP 6

In the slope-intercept form y=mx+by = mx + by=mx+b, mmm represents the **slope**.In our equation y=−x+2y = -x + 2y=−x+2, the coefficient of xxx is −1-1−1, so our **slope** is m=−1m = -1m=−1.Boom!

STEP 7

The *x*-intercept is where the line crosses the *x*-axis, meaning y=0y = 0y=0.Let's **substitute** y=0y = 0y=0 into our equation: 0=−x+20 = -x + 20=−x+2

STEP 8

Now, we **solve** for xxx.We can **add** xxx to both sides: x=2x = 2x=2 So, the **x-intercept** is 222.

STEP 9

In the slope-intercept form y=mx+by = mx + by=mx+b, bbb represents the *y*-intercept.In our equation y=−x+2y = -x + 2y=−x+2, b=2b = 2b=2.So, the **y-intercept** is 222.Awesome!

STEP 10

The **slope** is −1-1−1, the **x-intercept** is 222, and the **y-intercept** is 222.

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.

What is this asking? We need to find the slope, x-intercept, and y-intercept of a line given its equation. Watch out! Don't mix up the x and y intercepts!
Also, remember the slope-intercept form requires us to isolate $y$ .

1. Rewrite in slope-intercept form.
2. Identify the slope.
3. Calculate the x-intercept.
4. Calculate the y-intercept.

We start with $4x + 4y = 8$ .
To get to slope-intercept form, we want to isolate $y$ .
Let's subtract $4x$ from both sides of the equation: $4x + 4y - 4x = 8 - 4x$ $4y = 8 - 4x$

Now, we divide both sides by $4$ to completely isolate $y$ : $\frac{4y}{4} = \frac{8 - 4x}{4}$ $y = \frac{8}{4} - \frac{4x}{4}$ $y = 2 - x$

Finally, we rewrite the equation in the standard slope-intercept form $y = mx + b$ : $y = -x + 2$

In the slope-intercept form $y = mx + b$ , $m$ represents the slope.
In our equation $y = -x + 2$ , the coefficient of $x$ is $-1$ , so our slope is $m = -1$ .
Boom!

The x-intercept is where the line crosses the x-axis, meaning $y = 0$ .
Let's substitute $y = 0$ into our equation: $0 = -x + 2$

Now, we solve for $x$ .
We can add $x$ to both sides: $x = 2$ So, the x-intercept is $2$ .

In the slope-intercept form $y = mx + b$ , $b$ represents the y-intercept.
In our equation $y = -x + 2$ , $b = 2$ .
So, the y-intercept is $2$ .
Awesome!

The slope is $-1$ , the x-intercept is $2$ , and the y-intercept is $2$ .