Math  /  Algebra

QuestionFind the xx - and yy - interce
7. 12x+3y=12-12 x+3 y=12 x-int \qquad yy-int \qquad

Studdy Solution

STEP 1

What is this asking? We need to find where the line crosses the xx-axis and the yy-axis for the equation 12x+3y=12-12x + 3y = 12. Watch out! Don't forget that the xx-intercept is where y=0y = 0 and the yy-intercept is where x=0x = 0.

STEP 2

1. Find the xx-intercept
2. Find the yy-intercept

STEP 3

Alright, let's start by finding the xx-intercept!
Remember, this is where the line crosses the xx-axis, so y=0y = 0.
Let's substitute y=0y = 0 into the equation 12x+3y=12-12x + 3y = 12.
12x+3(0)=12-12x + 3(0) = 12

STEP 4

Simplify the equation.
Since 30=03 \cdot 0 = 0, we have:
12x=12-12x = 12

STEP 5

Now, let's solve for xx by dividing both sides by 12-12.
This helps us "divide to one" on the left side:
x=1212=1x = \frac{12}{-12} = -1So, the xx-intercept is at (1,0)(-1, 0).

STEP 6

Next, let's find the yy-intercept!
This is where the line crosses the yy-axis, so x=0x = 0.
Substitute x=0x = 0 into the equation:
12(0)+3y=12-12(0) + 3y = 12

STEP 7

Simplify the equation.
Since 120=0-12 \cdot 0 = 0, we have:
3y=123y = 12

STEP 8

Now, solve for yy by dividing both sides by 33.
This helps us "divide to one" on the left side:
y=123=4y = \frac{12}{3} = 4So, the yy-intercept is at (0,4)(0, 4).

STEP 9

The xx-intercept is (1,0)(-1, 0) and the yy-intercept is (0,4)(0, 4).

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