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Math  /  Algebra

QuestionRewrite the following equation in slope-intercept form. 13x+12y=−713 x+12 y=-7
Write your answer using integers, proper fractions, and improper fractions in simplest form. □\square Snbmit

Studdy Solution

STEP 1

What is this asking? We're asked to rewrite an equation from *standard form* to *slope-intercept form*.
Slope-intercept form is when we've solved for yy in terms of xx, so we can easily see the slope and the y-intercept! Watch out! Don't forget to fully simplify fractions and keep track of those negative signs!

STEP 2

1. Isolate the y-term
2. Solve for y

STEP 3

We're starting with 13x+12y=−713x + 12y = -7.
Our goal is to get yy by itself.

STEP 4

To get the yy term alone, we need to move the 13x13x to the other side.
We can do that by subtracting 13x13x from both sides of the equation: 13x+12y−13x=−7−13x13x + 12y - 13x = -7 - 13x 12y=−13x−712y = -13x - 7Remember, adding to zero is a powerful tool!

STEP 5

Now, we want to isolate yy.
Since yy is multiplied by **12**, we can divide both sides of the equation by **12**: 12y12=−13x−712 \frac{12y}{12} = \frac{-13x - 7}{12} Dividing to one is the key!

STEP 6

Now, let's simplify! y=−13x12−712 y = \frac{-13x}{12} - \frac{7}{12} y=−1312x−712 y = -\frac{13}{12}x - \frac{7}{12} Look at that, it's in slope-intercept form!

STEP 7

Our equation in slope-intercept form is y=−1312x−712y = -\frac{13}{12}x - \frac{7}{12}.

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