Math / Algebra

QuestionA line passes through the points $(-1,2)$ and $(3,18)$ . Write its equation in slope-intercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form. $\square$ 믐

Studdy Solution

STEP 1

What is this asking? We need to find the equation of a line that goes through two specific points and write it in a way that shows the slope and where the line crosses the y-axis. Watch out! Don't mix up the $x$ and $y$ coordinates when calculating the slope!
Also, remember that "simplest form" means no common factors in the fractions.

STEP 2

1. Calculate the Slope
2. Determine the Y-intercept
3. Write the Equation

STEP 3

Alright, let's kick things off by finding the slope of our line!
Remember, the slope tells us how steep the line is.
It's the rise over run, or the change in $y$ divided by the change in $x$ .

STEP 4

We've got two points: $(-1, 2)$ and $(3, 18)$ .
Let's label them!
Let $(-1, 2)$ be $(x_1, y_1)$ and $(3, 18)$ be $(x_2, y_2)$ .

STEP 5

The slope formula is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Let's plug in our values: $m = \frac{18 - 2}{3 - (-1)}$

STEP 6

Simplify the numerator and denominator: $m = \frac{16}{3 + 1} = \frac{16}{4}$

STEP 7

Now, let's simplify the fraction: $m = \frac{16}{4} = 4$ So, our slope is $m = 4$ !
Awesome!

STEP 8

Next up, the y-intercept!
This is the point where our line crosses the y-axis.
We can find it using the slope-intercept form of a linear equation: $y = mx + b$ where $m$ is the slope (which we just found!) and $b$ is the y-intercept.

STEP 9

We can plug in one of our points and the slope to solve for $b$ .
Let's use the point $(-1, 2)$ : $2 = 4(-1) + b$

STEP 10

Simplify and solve for $b$ : $2 = -4 + b$ Add 4 to both sides: $2 + 4 = -4 + 4 + b$ $6 = b$ So, our y-intercept is $b = 6$ !

STEP 11

We've got our slope ( $m = 4$ ) and our y-intercept ( $b = 6$ ).
Now, we just need to plug them into the slope-intercept form: $y = mx + b$

STEP 12

Substitute the values: $y = 4x + 6$ And there we have it!

STEP 13

The equation of the line in slope-intercept form is $y = 4x + 6$ .

Was this helpful?

QuestionA line passes through the points $(-1,2)$ and $(3,18)$ . Write its equation in slope-intercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form. $\square$ 믐

Studdy Solution

STEP 1

STEP 2

1. Calculate the Slope
2. Determine the Y-intercept
3. Write the Equation

STEP 3

Alright, let's kick things off by finding the slope of our line!
Remember, the slope tells us how steep the line is.
It's the rise over run, or the change in $y$ divided by the change in $x$ .

STEP 4

We've got two points: $(-1, 2)$ and $(3, 18)$ .
Let's label them!
Let $(-1, 2)$ be $(x_1, y_1)$ and $(3, 18)$ be $(x_2, y_2)$ .

STEP 5

The slope formula is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Let's plug in our values: $m = \frac{18 - 2}{3 - (-1)}$

STEP 6

Simplify the numerator and denominator: $m = \frac{16}{3 + 1} = \frac{16}{4}$

STEP 7

Now, let's simplify the fraction: $m = \frac{16}{4} = 4$ So, our slope is $m = 4$ !
Awesome!

STEP 8

Next up, the y-intercept!
This is the point where our line crosses the y-axis.
We can find it using the slope-intercept form of a linear equation: $y = mx + b$ where $m$ is the slope (which we just found!) and $b$ is the y-intercept.

STEP 9

We can plug in one of our points and the slope to solve for $b$ .
Let's use the point $(-1, 2)$ : $2 = 4(-1) + b$

STEP 10

Simplify and solve for $b$ : $2 = -4 + b$ Add 4 to both sides: $2 + 4 = -4 + 4 + b$ $6 = b$ So, our y-intercept is $b = 6$ !

STEP 11

We've got our slope ( $m = 4$ ) and our y-intercept ( $b = 6$ ).
Now, we just need to plug them into the slope-intercept form: $y = mx + b$

STEP 12

Substitute the values: $y = 4x + 6$ And there we have it!

STEP 13

The equation of the line in slope-intercept form is $y = 4x + 6$ .

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 passes through the points (−1,2)(-1,2)(−1,2) and (3,18)(3,18)(3,18). Write its equation in slope-intercept form.Write your answer using integers, proper fractions, and improper fractions in simplest form. □\square□ 믐

Studdy Solution

STEP 1

STEP 2

1. Calculate the Slope2. Determine the Y-intercept3. Write the Equation

STEP 3

Alright, let's **kick things off** by finding the slope of our line!Remember, the slope tells us how steep the line is.It's the **rise over run**, or the change in yyy divided by the change in xxx.

STEP 4

We've got two points: (−1,2)(-1, 2)(−1,2) and (3,18)(3, 18)(3,18).Let's label them!Let (−1,2)(-1, 2)(−1,2) be (x1,y1)(x_1, y_1)(x1​,y1​) and (3,18)(3, 18)(3,18) be (x2,y2)(x_2, y_2)(x2​,y2​).

STEP 5

The **slope formula** is: m=y2−y1x2−x1 m = \frac{y_2 - y_1}{x_2 - x_1} m=x2​−x1​y2​−y1​​ Let's **plug in** our values: m=18−23−(−1) m = \frac{18 - 2}{3 - (-1)} m=3−(−1)18−2​

STEP 6

**Simplify** the numerator and denominator: m=163+1=164 m = \frac{16}{3 + 1} = \frac{16}{4} m=3+116​=416​

STEP 7

Now, let's **simplify the fraction**: m=164=4 m = \frac{16}{4} = 4 m=416​=4 So, our **slope** is m=4m = 4m=4!Awesome!

STEP 8

Next up, the **y-intercept**!This is the point where our line crosses the y-axis.We can find it using the **slope-intercept form** of a linear equation: y=mx+b y = mx + b y=mx+b where mmm is the slope (which we just found!) and bbb is the y-intercept.

STEP 9

We can **plug in** one of our points and the slope to solve for bbb.Let's use the point (−1,2)(-1, 2)(−1,2): 2=4(−1)+b 2 = 4(-1) + b 2=4(−1)+b

STEP 10

**Simplify** and **solve for** bbb: 2=−4+b 2 = -4 + b 2=−4+b Add 4 to both sides: 2+4=−4+4+b 2 + 4 = -4 + 4 + b 2+4=−4+4+b 6=b 6 = b 6=bSo, our **y-intercept** is b=6b = 6b=6!

STEP 11

We've got our **slope** (m=4m = 4m=4) and our **y-intercept** (b=6b = 6b=6).Now, we just need to **plug them into** the slope-intercept form: y=mx+b y = mx + b y=mx+b

STEP 12

**Substitute** the values: y=4x+6 y = 4x + 6 y=4x+6 And there we have it!

STEP 13

The equation of the line in slope-intercept form is y=4x+6y = 4x + 6y=4x+6.

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 passes through the points $(-1,2)$ and $(3,18)$ . Write its equation in slope-intercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form. $\square$ 믐

1. Calculate the Slope
2. Determine the Y-intercept
3. Write the Equation

Alright, let's kick things off by finding the slope of our line!
Remember, the slope tells us how steep the line is.
It's the rise over run, or the change in $y$ divided by the change in $x$ .

We've got two points: $(-1, 2)$ and $(3, 18)$ .
Let's label them!
Let $(-1, 2)$ be $(x_1, y_1)$ and $(3, 18)$ be $(x_2, y_2)$ .

The slope formula is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Let's plug in our values: $m = \frac{18 - 2}{3 - (-1)}$

Simplify the numerator and denominator: $m = \frac{16}{3 + 1} = \frac{16}{4}$

Now, let's simplify the fraction: $m = \frac{16}{4} = 4$ So, our slope is $m = 4$ !
Awesome!

Next up, the y-intercept!
This is the point where our line crosses the y-axis.
We can find it using the slope-intercept form of a linear equation: $y = mx + b$ where $m$ is the slope (which we just found!) and $b$ is the y-intercept.

We can plug in one of our points and the slope to solve for $b$ .
Let's use the point $(-1, 2)$ : $2 = 4(-1) + b$

Simplify and solve for $b$ : $2 = -4 + b$ Add 4 to both sides: $2 + 4 = -4 + 4 + b$ $6 = b$ So, our y-intercept is $b = 6$ !

We've got our slope ( $m = 4$ ) and our y-intercept ( $b = 6$ ).
Now, we just need to plug them into the slope-intercept form: $y = mx + b$

Substitute the values: $y = 4x + 6$ And there we have it!

The equation of the line in slope-intercept form is $y = 4x + 6$ .