Math / Algebra

QuestionA line passes through the points $(-8,-13)$ and $(11,-13)$ . 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 goes through two given points and write it in slope-intercept form, which looks like $y = mx + b$ . Watch out! A horizontal line has a slope of zero, and a vertical line has an undefined slope.
Don't mix these up!

STEP 2

1. Calculate the slope.
2. Determine the y-intercept.
3. Write the equation.

STEP 3

Let's dive in by finding the slope!
The slope ( $m$ ) is the change in $y$ divided by the change in $x$ .
Our points are $(-8, -13)$ and $(11, -13)$ .

STEP 4

The change in $y$ is $(-13) - (-13) = 0$ .
The change in $x$ is $11 - (-8) = 19$ .

STEP 5

So, our slope $m$ is $\frac{0}{19} = 0$ .
A zero slope means we have a horizontal line!

STEP 6

Since our line is horizontal, the $y$ -value is the same for every point on the line.
We already know that both of our points have a $y$ -value of $-13$ .
This tells us that our line must cross the $y$ -axis at $-13$ .

STEP 7

So, our y-intercept ( $b$ ) is $-13$ .

STEP 8

We've got our slope ( $m = 0$ ) and our y-intercept ( $b = -13$ ).
Let's plug these values into the slope-intercept form: $y = mx + b$ .

STEP 9

This gives us $y = (0)x + (-13)$ , which simplifies to $y = -13$ .
And there we have it, the equation of our line!

STEP 10

The equation of the line in slope-intercept form is $y = -13$ .

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QuestionA line passes through the points $(-8,-13)$ and $(11,-13)$ . 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 goes through two given points and write it in slope-intercept form, which looks like $y = mx + b$ . Watch out! A horizontal line has a slope of zero, and a vertical line has an undefined slope.
Don't mix these up!

STEP 2

1. Calculate the slope.
2. Determine the y-intercept.
3. Write the equation.

STEP 3

Let's dive in by finding the slope!
The slope ( $m$ ) is the change in $y$ divided by the change in $x$ .
Our points are $(-8, -13)$ and $(11, -13)$ .

STEP 4

The change in $y$ is $(-13) - (-13) = 0$ .
The change in $x$ is $11 - (-8) = 19$ .

STEP 5

So, our slope $m$ is $\frac{0}{19} = 0$ .
A zero slope means we have a horizontal line!

STEP 6

Since our line is horizontal, the $y$ -value is the same for every point on the line.
We already know that both of our points have a $y$ -value of $-13$ .
This tells us that our line must cross the $y$ -axis at $-13$ .

STEP 7

So, our y-intercept ( $b$ ) is $-13$ .

STEP 8

We've got our slope ( $m = 0$ ) and our y-intercept ( $b = -13$ ).
Let's plug these values into the slope-intercept form: $y = mx + b$ .

STEP 9

This gives us $y = (0)x + (-13)$ , which simplifies to $y = -13$ .
And there we have it, the equation of our line!

STEP 10

The equation of the line in slope-intercept form is $y = -13$ .

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QuestionA line passes through the points (−8,−13)(-8,-13)(−8,−13) and (11,−13)(11,-13)(11,−13). 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 goes through two given points and write it in slope-intercept form, which looks like y=mx+by = mx + by=mx+b. Watch out! A horizontal line has a slope of zero, and a vertical line has an undefined slope.Don't mix these up!

STEP 2

1. Calculate the slope.2. Determine the y-intercept.3. Write the equation.

STEP 3

Let's **dive in** by finding the slope!The slope (mmm) is the **change in** yyy divided by the **change in** xxx.Our points are (−8,−13)(-8, -13)(−8,−13) and (11,−13)(11, -13)(11,−13).

STEP 4

The **change in** yyy is (−13)−(−13)=0(-13) - (-13) = 0(−13)−(−13)=0.The **change in** xxx is 11−(−8)=1911 - (-8) = 1911−(−8)=19.

STEP 5

So, our slope mmm is 019=0\frac{0}{19} = 0190​=0.A **zero slope** means we have a horizontal line!

STEP 6

Since our line is horizontal, the yyy-value is the same for *every* point on the line.We already know that both of our points have a yyy-value of −13-13−13.This tells us that our line *must* cross the yyy-axis at −13-13−13.

STEP 7

So, our **y-intercept** (bbb) is −13-13−13.

STEP 8

We've got our slope (m=0m = 0m=0) and our y-intercept (b=−13b = -13b=−13).Let's **plug these values** into the slope-intercept form: y=mx+by = mx + by=mx+b.

STEP 9

This gives us y=(0)x+(−13)y = (0)x + (-13)y=(0)x+(−13), which simplifies to y=−13y = -13y=−13.And there we have it, the equation of our line!

STEP 10

The equation of the line in slope-intercept form is y=−13y = -13y=−13.

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Start learning now

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

QuestionA line passes through the points $(-8,-13)$ and $(11,-13)$ . 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 goes through two given points and write it in slope-intercept form, which looks like $y = mx + b$ . Watch out! A horizontal line has a slope of zero, and a vertical line has an undefined slope.
Don't mix these up!

1. Calculate the slope.
2. Determine the y-intercept.
3. Write the equation.

Let's dive in by finding the slope!
The slope ( $m$ ) is the change in $y$ divided by the change in $x$ .
Our points are $(-8, -13)$ and $(11, -13)$ .

The change in $y$ is $(-13) - (-13) = 0$ .
The change in $x$ is $11 - (-8) = 19$ .

So, our slope $m$ is $\frac{0}{19} = 0$ .
A zero slope means we have a horizontal line!

Since our line is horizontal, the $y$ -value is the same for every point on the line.
We already know that both of our points have a $y$ -value of $-13$ .
This tells us that our line must cross the $y$ -axis at $-13$ .

So, our y-intercept ( $b$ ) is $-13$ .

We've got our slope ( $m = 0$ ) and our y-intercept ( $b = -13$ ).
Let's plug these values into the slope-intercept form: $y = mx + b$ .

This gives us $y = (0)x + (-13)$ , which simplifies to $y = -13$ .
And there we have it, the equation of our line!

The equation of the line in slope-intercept form is $y = -13$ .