QuestionRewrite the following equation in slope-intercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Studdy Solution
STEP 1
What is this asking? We need to rewrite the equation so it looks like , where is the slope and is the y-intercept. Watch out! Don't forget to simplify the fractions completely!
STEP 2
1. Isolate
2. Simplify
STEP 3
Alright, so we've got this equation and we want to get all by itself.
It's like is trapped in a cage guarded by a **13**, and we need to set it free!
STEP 4
Since is being multiplied by **13**, we need to do the *opposite* operation to both sides of the equation to get rid of it.
The opposite of multiplication is division, so let's divide *both* sides by **13**!
This is totally allowed because as long as we do the same thing to both sides of the equation, everything stays balanced.
STEP 5
STEP 6
On the left side, the **13**s divide to one, leaving us with just , which is exactly what we wanted!
STEP 7
STEP 8
Now, we can split the fraction on the right side into two separate fractions.
This will make it easier to see the slope and the y-intercept.
STEP 9
STEP 10
Let's check if our fractions can be simplified.
Can be simplified any further?
Nope! **2** and **13** don't share any common factors other than 1.
STEP 11
What about attached to the ?
Nope, same deal!
It's already in simplest form.
STEP 12
So, our equation is already simplified!
Awesome!
STEP 13
Our **slope**, , is , and our **y-intercept**, , is .
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