Math / Algebra

QuestionA line has a slope of 0 and passes through the point $(4,4)$ . Write its equation in slopeintercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form. $\square$

Studdy Solution

STEP 1

What is this asking? We need to find the equation of a line that is flat (because the slope is zero) and goes through the point ( $4,4$ ). Watch out! A slope of zero doesn't mean there's no line at all!
It just means the line is perfectly horizontal.

STEP 2

1. Understand Slope-Intercept Form
2. Plug in the Slope
3. Find the y-intercept
4. Write the Final Equation

STEP 3

Let's remember what slope-intercept form looks like: $y = mx + b$ .
Here, $m$ is the slope of the line, and $b$ is the y-intercept (where the line crosses the y-axis).

STEP 4

We're given that the slope is zero, so $m = 0$ .
Let's plug that into our equation: $y = 0 \cdot x + b$ .

STEP 5

Simplifying, we get $y = b$ .
So, whatever the y-intercept is, that's what $y$ will always be!

STEP 6

We know the line passes through the point ( $4,4$ ).
This means when $x = 4$ , $y = 4$ .
Let's plug these values into our simplified equation: $4 = b$ .

STEP 7

Wow, that was easy!
We found our y-intercept: $b = 4$ .

STEP 8

Now we have everything we need!
We know $b = 4$ , so our equation is $y = 4$ .

STEP 9

The equation of the line is $y = 4$ .

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QuestionA line has a slope of 0 and passes through the point $(4,4)$ . Write its equation in slopeintercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form. $\square$

Studdy Solution

STEP 1

What is this asking? We need to find the equation of a line that is flat (because the slope is zero) and goes through the point ( $4,4$ ). Watch out! A slope of zero doesn't mean there's no line at all!
It just means the line is perfectly horizontal.

STEP 2

1. Understand Slope-Intercept Form
2. Plug in the Slope
3. Find the y-intercept
4. Write the Final Equation

STEP 3

Let's remember what slope-intercept form looks like: $y = mx + b$ .
Here, $m$ is the slope of the line, and $b$ is the y-intercept (where the line crosses the y-axis).

STEP 4

We're given that the slope is zero, so $m = 0$ .
Let's plug that into our equation: $y = 0 \cdot x + b$ .

STEP 5

Simplifying, we get $y = b$ .
So, whatever the y-intercept is, that's what $y$ will always be!

STEP 6

We know the line passes through the point ( $4,4$ ).
This means when $x = 4$ , $y = 4$ .
Let's plug these values into our simplified equation: $4 = b$ .

STEP 7

Wow, that was easy!
We found our y-intercept: $b = 4$ .

STEP 8

Now we have everything we need!
We know $b = 4$ , so our equation is $y = 4$ .

STEP 9

The equation of the line is $y = 4$ .

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QuestionA line has a slope of 0 and passes through the point (4,4)(4,4)(4,4). Write its equation in slopeintercept form.Write your answer using integers, proper fractions, and improper fractions in simplest form. □\square□

Studdy Solution

STEP 1

What is this asking? We need to find the equation of a line that is flat (because the slope is zero) and goes through the point (4,44,44,4). Watch out! A slope of zero doesn't mean there's no line at all!It just means the line is perfectly horizontal.

STEP 2

1. Understand Slope-Intercept Form2. Plug in the Slope3. Find the y-intercept4. Write the Final Equation

STEP 3

Let's remember what slope-intercept form looks like: y=mx+by = mx + by=mx+b.Here, mmm is the **slope** of the line, and bbb is the **y-intercept** (where the line crosses the y-axis).

STEP 4

We're given that the slope is **zero**, so m=0m = 0m=0.Let's plug that into our equation: y=0⋅x+by = 0 \cdot x + by=0⋅x+b.

STEP 5

Simplifying, we get y=by = by=b.So, whatever the y-intercept is, that's what yyy will always be!

STEP 6

We know the line passes through the point (4,44,44,4).This means when x=4x = 4x=4, y=4y = 4y=4.Let's plug these values into our simplified equation: 4=b4 = b4=b.

STEP 7

Wow, that was easy!We found our **y-intercept**: b=4b = 4b=4.

STEP 8

Now we have everything we need!We know b=4b = 4b=4, so our equation is y=4y = 4y=4.

STEP 9

The equation of the line is y=4y = 4y=4.

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.

QuestionA line has a slope of 0 and passes through the point $(4,4)$ . Write its equation in slopeintercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form. $\square$

What is this asking? We need to find the equation of a line that is flat (because the slope is zero) and goes through the point ( $4,4$ ). Watch out! A slope of zero doesn't mean there's no line at all!
It just means the line is perfectly horizontal.

1. Understand Slope-Intercept Form
2. Plug in the Slope
3. Find the y-intercept
4. Write the Final Equation

Let's remember what slope-intercept form looks like: $y = mx + b$ .
Here, $m$ is the slope of the line, and $b$ is the y-intercept (where the line crosses the y-axis).

We're given that the slope is zero, so $m = 0$ .
Let's plug that into our equation: $y = 0 \cdot x + b$ .

Simplifying, we get $y = b$ .
So, whatever the y-intercept is, that's what $y$ will always be!

We know the line passes through the point ( $4,4$ ).
This means when $x = 4$ , $y = 4$ .
Let's plug these values into our simplified equation: $4 = b$ .

Wow, that was easy!
We found our y-intercept: $b = 4$ .

Now we have everything we need!
We know $b = 4$ , so our equation is $y = 4$ .

The equation of the line is $y = 4$ .