Math / Algebra

Question2 D. 3 Write the equation of a linear function Video
A line passes through the points $(-1,6)$ and $(1,-6)$ . Write its equation in slope-intercept form. Write your answer using integers, proper fractions, and improper fractions in simplest form. $\square$ Submit

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 is $y = mx + b$ . Watch out! Don't mix up the $x$ and $y$ coordinates!
Also, remember to simplify the fraction in the final equation.

STEP 2

1. Find the slope
2. Find the y-intercept
3. Write the equation

STEP 3

Alright, let's start by finding the slope!
The slope, which we call $m$ , tells us how steep our line is.
We can find it using the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ where $(x_1, y_1)$ and $(x_2, y_2)$ are our two points.

STEP 4

Let's label our points.
We'll call $(-1, 6)$ as point 1, so $x_1 = -1$ and $y_1 = 6$ .
And $(1, -6)$ will be point 2, so $x_2 = 1$ and $y_2 = -6$ .

STEP 5

Now, let's plug these values into our slope formula: $m = \frac{-6 - 6}{1 - (-1)}$

STEP 6

Simplify the numerator and the denominator: $m = \frac{-12}{1 + 1} = \frac{-12}{2}$

STEP 7

Divide $-12$ by $2$ to get our slope: $m = -6$ So, our line has a slope of $-6$ , meaning it goes downwards pretty steeply!

STEP 8

Great, we've got our slope!
Now, let's find the y-intercept, which we call $b$ .
This is the point where our line crosses the y-axis.
We can use the slope-intercept form of a linear equation, $y = mx + b$ , and plug in one of our points and the slope we just found.

STEP 9

Let's use point 1, $(-1, 6)$ , and our slope, $m = -6$ . Substitute these values into the equation: $6 = (-6)(-1) + b$

STEP 10

Simplify the equation: $6 = 6 + b$

STEP 11

To isolate $b$ , we can add $-6$ to both sides of the equation: $6 + (-6) = 6 + b + (-6)$ $0 = b$

STEP 12

So, our y-intercept is $b = 0$ .
This means our line goes right through the origin!

STEP 13

We have our slope, $m = -6$ , and our y-intercept, $b = 0$ .
Now, we just need to plug these values back into the slope-intercept form, $y = mx + b$ .

STEP 14

Substitute the values: $y = (-6)x + 0$

STEP 15

Simplify: $y = -6x$

STEP 16

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

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Question2 D. 3 Write the equation of a linear function Video
A line passes through the points $(-1,6)$ and $(1,-6)$ . Write its equation in slope-intercept form. Write your answer using integers, proper fractions, and improper fractions in simplest form. $\square$ Submit

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 is $y = mx + b$ . Watch out! Don't mix up the $x$ and $y$ coordinates!
Also, remember to simplify the fraction in the final equation.

STEP 2

1. Find the slope
2. Find the y-intercept
3. Write the equation

STEP 3

Alright, let's start by finding the slope!
The slope, which we call $m$ , tells us how steep our line is.
We can find it using the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ where $(x_1, y_1)$ and $(x_2, y_2)$ are our two points.

STEP 4

Let's label our points.
We'll call $(-1, 6)$ as point 1, so $x_1 = -1$ and $y_1 = 6$ .
And $(1, -6)$ will be point 2, so $x_2 = 1$ and $y_2 = -6$ .

STEP 5

Now, let's plug these values into our slope formula: $m = \frac{-6 - 6}{1 - (-1)}$

STEP 6

Simplify the numerator and the denominator: $m = \frac{-12}{1 + 1} = \frac{-12}{2}$

STEP 7

Divide $-12$ by $2$ to get our slope: $m = -6$ So, our line has a slope of $-6$ , meaning it goes downwards pretty steeply!

STEP 8

Great, we've got our slope!
Now, let's find the y-intercept, which we call $b$ .
This is the point where our line crosses the y-axis.
We can use the slope-intercept form of a linear equation, $y = mx + b$ , and plug in one of our points and the slope we just found.

STEP 9

Let's use point 1, $(-1, 6)$ , and our slope, $m = -6$ . Substitute these values into the equation: $6 = (-6)(-1) + b$

STEP 10

Simplify the equation: $6 = 6 + b$

STEP 11

To isolate $b$ , we can add $-6$ to both sides of the equation: $6 + (-6) = 6 + b + (-6)$ $0 = b$

STEP 12

So, our y-intercept is $b = 0$ .
This means our line goes right through the origin!

STEP 13

We have our slope, $m = -6$ , and our y-intercept, $b = 0$ .
Now, we just need to plug these values back into the slope-intercept form, $y = mx + b$ .

STEP 14

Substitute the values: $y = (-6)x + 0$

STEP 15

Simplify: $y = -6x$

STEP 16

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

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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 is y=mx+by = mx + by=mx+b. Watch out! Don't mix up the xxx and yyy coordinates!Also, remember to simplify the fraction in the final equation.

STEP 2

1. Find the slope2. Find the y-intercept3. Write the equation

STEP 3

STEP 4

Let's **label** our points.We'll call (−1,6)(-1, 6)(−1,6) as point 1, so x1=−1x_1 = -1x1​=−1 and y1=6y_1 = 6y1​=6.And (1,−6)(1, -6)(1,−6) will be point 2, so x2=1x_2 = 1x2​=1 and y2=−6y_2 = -6y2​=−6.

STEP 5

Now, let's **plug** these values into our **slope formula**: m=−6−61−(−1) m = \frac{-6 - 6}{1 - (-1)} m=1−(−1)−6−6​

STEP 6

**Simplify** the numerator and the denominator: m=−121+1=−122 m = \frac{-12}{1 + 1} = \frac{-12}{2} m=1+1−12​=2−12​

STEP 7

**Divide** −12-12−12 by 222 to get our **slope**: m=−6 m = -6 m=−6 So, our line has a slope of −6-6−6, meaning it goes downwards pretty steeply!

STEP 8

Great, we've got our slope!Now, let's find the **y-intercept**, which we call bbb.This is the point where our line crosses the y-axis.We can use the slope-intercept form of a linear equation, y=mx+by = mx + by=mx+b, and plug in one of our points and the slope we just found.

STEP 9

Let's use point 1, (−1,6)(-1, 6)(−1,6), and our slope, m=−6m = -6m=−6. **Substitute** these values into the equation: 6=(−6)(−1)+b 6 = (-6)(-1) + b 6=(−6)(−1)+b

STEP 10

**Simplify** the equation: 6=6+b 6 = 6 + b 6=6+b

STEP 11

To **isolate** bbb, we can add −6-6−6 to both sides of the equation: 6+(−6)=6+b+(−6) 6 + (-6) = 6 + b + (-6) 6+(−6)=6+b+(−6) 0=b 0 = b 0=b

STEP 12

So, our **y-intercept** is b=0b = 0b=0.This means our line goes right through the origin!

STEP 13

We have our **slope**, m=−6m = -6m=−6, and our **y-intercept**, b=0b = 0b=0.Now, we just need to **plug** these values back into the slope-intercept form, y=mx+by = mx + by=mx+b.

STEP 14

**Substitute** the values: y=(−6)x+0 y = (-6)x + 0 y=(−6)x+0

STEP 15

**Simplify**: y=−6x y = -6x y=−6x

STEP 16

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

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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 is $y = mx + b$ . Watch out! Don't mix up the $x$ and $y$ coordinates!
Also, remember to simplify the fraction in the final equation.

1. Find the slope
2. Find the y-intercept
3. Write the equation

Let's label our points.
We'll call $(-1, 6)$ as point 1, so $x_1 = -1$ and $y_1 = 6$ .
And $(1, -6)$ will be point 2, so $x_2 = 1$ and $y_2 = -6$ .

Now, let's plug these values into our slope formula: $m = \frac{-6 - 6}{1 - (-1)}$

Simplify the numerator and the denominator: $m = \frac{-12}{1 + 1} = \frac{-12}{2}$

Divide $-12$ by $2$ to get our slope: $m = -6$ So, our line has a slope of $-6$ , meaning it goes downwards pretty steeply!

Great, we've got our slope!
Now, let's find the y-intercept, which we call $b$ .
This is the point where our line crosses the y-axis.
We can use the slope-intercept form of a linear equation, $y = mx + b$ , and plug in one of our points and the slope we just found.

Let's use point 1, $(-1, 6)$ , and our slope, $m = -6$ . Substitute these values into the equation: $6 = (-6)(-1) + b$

Simplify the equation: $6 = 6 + b$

To isolate $b$ , we can add $-6$ to both sides of the equation: $6 + (-6) = 6 + b + (-6)$ $0 = b$

So, our y-intercept is $b = 0$ .
This means our line goes right through the origin!

We have our slope, $m = -6$ , and our y-intercept, $b = 0$ .
Now, we just need to plug these values back into the slope-intercept form, $y = mx + b$ .

Substitute the values: $y = (-6)x + 0$

Simplify: $y = -6x$

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