Math / Algebra

QuestionLearn with an example • or Watch a video (b)
A line has a slope of 8 and passes through the point $(1,3)$ . 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, specifically in slope-intercept form, given its slope and a point it passes through. Watch out! Remember slope-intercept form is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept, not the x-intercept!

STEP 2

1. Set up the equation with the given slope.
2. Plug in the given point to find the y-intercept.
3. Write the final equation.

STEP 3

We're given that the slope of our line is 8.
Remember, the slope-intercept form of a line is $y = mx + b$ , where $m$ is the slope.
So, we can plug in our slope to get $y = 8x + b$ .
We're halfway there!

STEP 4

We know the line passes through the point $(1, 3)$ .
This means when $x = 1$ , $y = 3$ .
Let's substitute these values into our equation $y = 8x + b$ : $3 = 8 \cdot 1 + b$

STEP 5

Now, let's solve for $b$ ! $3 = 8 + b$ To isolate $b$ , we can add $-8$ to both sides of the equation: $3 + (-8) = 8 + (-8) + b$ $-5 = b$ So, our y-intercept is $-5$ .

STEP 6

We found that $m = 8$ and $b = -5$ .
Let's plug these values back into the slope-intercept form $y = mx + b$ .

STEP 7

This gives us the final equation: $y = 8x + (-5)$ or $y = 8x - 5$ .
Awesome!

STEP 8

The equation of the line in slope-intercept form is $y = 8x - 5$ .

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QuestionLearn with an example • or Watch a video (b)
A line has a slope of 8 and passes through the point $(1,3)$ . 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, specifically in slope-intercept form, given its slope and a point it passes through. Watch out! Remember slope-intercept form is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept, not the x-intercept!

STEP 2

1. Set up the equation with the given slope.
2. Plug in the given point to find the y-intercept.
3. Write the final equation.

STEP 3

We're given that the slope of our line is 8.
Remember, the slope-intercept form of a line is $y = mx + b$ , where $m$ is the slope.
So, we can plug in our slope to get $y = 8x + b$ .
We're halfway there!

STEP 4

We know the line passes through the point $(1, 3)$ .
This means when $x = 1$ , $y = 3$ .
Let's substitute these values into our equation $y = 8x + b$ : $3 = 8 \cdot 1 + b$

STEP 5

Now, let's solve for $b$ ! $3 = 8 + b$ To isolate $b$ , we can add $-8$ to both sides of the equation: $3 + (-8) = 8 + (-8) + b$ $-5 = b$ So, our y-intercept is $-5$ .

STEP 6

We found that $m = 8$ and $b = -5$ .
Let's plug these values back into the slope-intercept form $y = mx + b$ .

STEP 7

This gives us the final equation: $y = 8x + (-5)$ or $y = 8x - 5$ .
Awesome!

STEP 8

The equation of the line in slope-intercept form is $y = 8x - 5$ .

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QuestionLearn with an example • or Watch a video (b)A line has a slope of 8 and passes through the point (1,3)(1,3)(1,3). 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, specifically in slope-intercept form, given its slope and a point it passes through. Watch out! Remember slope-intercept form is y=mx+by = mx + by=mx+b, where mmm is the slope and bbb is the y-intercept, not the x-intercept!

STEP 2

1. Set up the equation with the given slope.2. Plug in the given point to find the y-intercept.3. Write the final equation.

STEP 3

We're given that the slope of our line is **8**.Remember, the slope-intercept form of a line is y=mx+by = mx + by=mx+b, where mmm is the slope.So, we can **plug in** our slope to get y=8x+by = 8x + by=8x+b.We're halfway there!

STEP 4

We know the line passes through the point (1,3)(1, 3)(1,3).This means when x=1x = 1x=1, y=3y = 3y=3.Let's **substitute** these values into our equation y=8x+by = 8x + by=8x+b: 3=8⋅1+b3 = 8 \cdot 1 + b3=8⋅1+b

STEP 5

Now, let's **solve for** bbb! 3=8+b3 = 8 + b3=8+b To **isolate** bbb, we can add −8 -8 −8 to both sides of the equation: 3+(−8)=8+(−8)+b3 + (-8) = 8 + (-8) + b3+(−8)=8+(−8)+b −5=b-5 = b−5=bSo, our **y-intercept** is −5-5−5.

STEP 6

We found that m=8m = 8m=8 and b=−5b = -5b=−5.Let's **plug these values back** into the slope-intercept form y=mx+by = mx + by=mx+b.

STEP 7

This gives us the **final equation**: y=8x+(−5)y = 8x + (-5)y=8x+(−5) or y=8x−5y = 8x - 5y=8x−5.Awesome!

STEP 8

The equation of the line in slope-intercept form is y=8x−5y = 8x - 5y=8x−5.

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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.

QuestionLearn with an example • or Watch a video (b)
A line has a slope of 8 and passes through the point $(1,3)$ . 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, specifically in slope-intercept form, given its slope and a point it passes through. Watch out! Remember slope-intercept form is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept, not the x-intercept!

1. Set up the equation with the given slope.
2. Plug in the given point to find the y-intercept.
3. Write the final equation.

We're given that the slope of our line is 8.
Remember, the slope-intercept form of a line is $y = mx + b$ , where $m$ is the slope.
So, we can plug in our slope to get $y = 8x + b$ .
We're halfway there!

We know the line passes through the point $(1, 3)$ .
This means when $x = 1$ , $y = 3$ .
Let's substitute these values into our equation $y = 8x + b$ : $3 = 8 \cdot 1 + b$

Now, let's solve for $b$ ! $3 = 8 + b$ To isolate $b$ , we can add $-8$ to both sides of the equation: $3 + (-8) = 8 + (-8) + b$ $-5 = b$ So, our y-intercept is $-5$ .

We found that $m = 8$ and $b = -5$ .
Let's plug these values back into the slope-intercept form $y = mx + b$ .

This gives us the final equation: $y = 8x + (-5)$ or $y = 8x - 5$ .
Awesome!

The equation of the line in slope-intercept form is $y = 8x - 5$ .