Math  /  Algebra

QuestionFind the xx-intercept and yy-intercept of the line. x2y=6x-2 y=-6 x -intercept: \square y -intercept: \square

Studdy Solution

STEP 1

What is this asking? We need to find the points where this line crosses the xx and yy axes! Watch out! Don't mix up the xx and yy intercepts!
Remember, the *xx-intercept* is where the line crosses the xx-axis, and the *yy-intercept* is where it crosses the yy-axis.

STEP 2

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

STEP 3

The **xx-intercept** is the xx value where the line crosses the xx-axis.
When a line crosses the xx-axis, the yy value is always **zero**.
So, we **substitute** y=0y = 0 into our equation: x20=6 x - 2 \cdot 0 = -6

STEP 4

Now, we **simplify** and **solve** for xx: x0=6 x - 0 = -6 x=6 x = -6

STEP 5

So, the **xx-intercept** is (6,0)(-6, 0).
Remember, the yy value is zero at the xx-intercept!

STEP 6

The **yy-intercept** is the yy value where the line crosses the yy-axis.
When a line crosses the yy-axis, the xx value is always **zero**.
So, we **substitute** x=0x = 0 into our original equation: 02y=6 0 - 2y = -6

STEP 7

Now, we **simplify** and **solve** for yy: 2y=6 -2y = -6

STEP 8

To **isolate** yy, we'll **divide** both sides of the equation by 2-2.
Remember, dividing by 2-2 is the same as multiplying by 12-\frac{1}{2}. 2y2=62 \frac{-2y}{-2} = \frac{-6}{-2} y=3 y = 3

STEP 9

So, the **yy-intercept** is (0,3)(0, 3).
Remember, the xx value is zero at the yy-intercept!

STEP 10

The xx-intercept is (6,0)(-6, 0) and the yy-intercept is (0,3)(0, 3).

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