Math  /  Algebra

QuestionA line passes through the points (5,15)(-5,15) and (6,18)(6,-18). Write its equation in slope-intercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form. \square

Studdy Solution

STEP 1

What is this asking? 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 xx and yy coordinates!
Also, remember to simplify your fractions to their lowest terms.

STEP 2

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

STEP 3

Alright, let's **kick things off** by finding the slope!
Remember, the slope is how steep the line is, and it's found by looking at the change in yy over the change in xx.
The formula for slope, often represented by the letter mm, is: m=y2y1x2x1 m = \frac{y_2 - y_1}{x_2 - x_1}

STEP 4

Our two points are (5,15)(-5, 15) and (6,18)(6, -18).
Let's **label** these points!
We'll call (5,15)(-5, 15) our **first point**, so x1=5x_1 = -5 and y1=15y_1 = 15.
And (6,18)(6, -18) will be our **second point**, making x2=6x_2 = 6 and y2=18y_2 = -18.

STEP 5

Now, let's **plug these values** into our slope formula: m=18156(5) m = \frac{-18 - 15}{6 - (-5)}

STEP 6

**Simplify** the numerator and denominator: m=336+5=3311 m = \frac{-33}{6 + 5} = \frac{-33}{11}

STEP 7

**Divide** 33-33 by 1111 to get our **slope**: m=3 m = -3 Woohoo! We've got our slope!

STEP 8

Next up, the y-intercept!
This is the point where our line **crosses** the y-axis, and it's represented by bb in our slope-intercept form, which looks like this: y=mx+b y = mx + b

STEP 9

We already know m=3m = -3, and we can use one of our points to find bb.
Let's use the **first point**, (5,15)(-5, 15), where x=5x = -5 and y=15y = 15. **Substitute** these values, along with our slope, into the slope-intercept equation: 15=(3)(5)+b 15 = (-3) \cdot (-5) + b

STEP 10

**Simplify** the equation: 15=15+b 15 = 15 + b

STEP 11

To **isolate** bb, let's add 15-15 to both sides of the equation: 15+(15)=15+(15)+b 15 + (-15) = 15 + (-15) + b 0=b 0 = b So, our y-intercept is b=0b = 0!

STEP 12

We have our **slope**, m=3m = -3, and our **y-intercept**, b=0b = 0.
Now, we just need to **plug them** into the slope-intercept form: y=mx+b y = mx + b y=3x+0 y = -3x + 0

STEP 13

Since adding zero doesn't change the value, we can **simplify** this to: y=3x y = -3x And there you have it!

STEP 14

y=3xy = -3x

Was this helpful?

Studdy solves anything!

banner

Start learning now

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

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord