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Math  /  Algebra

QuestionWhat is the x -intercept for this linear equation? 12x−23y=−6\frac{1}{2} x-\frac{2}{3} y=-6

Studdy Solution

STEP 1

What is this asking? Where does this line cross the x-axis? Watch out! Don't mix up x-intercepts and y-intercepts!
Remember, at the x-intercept, the y-value is always **zero**!

STEP 2

1. Set *y* to zero.
2. Solve for *x*.

STEP 3

Because the line crosses the x-axis when the y-value is **zero**!
This gives us the x-intercept.
Let's **substitute** (\$y = 0\$) into our equation:
12x−23y=−6\frac{1}{2}x - \frac{2}{3}y = -6 12x−23⋅0=−6\frac{1}{2}x - \frac{2}{3} \cdot 0 = -6

STEP 4

(Anything multiplied by **zero** is **zero**, so we can simplify the equation:
12x−0=−6\frac{1}{2}x - 0 = -6 12x=−6\frac{1}{2}x = -6

STEP 5

Now, we want to get \(\$x\$) all by itself. We can do this by **multiplying** both sides of the equation by **2**. Remember, we're multiplying by 2 to divide the left side by \(\frac{1}{2}, which is the same as multiplying by 2, and thus leaving us with just (\$x\$).
2⋅12x=2⋅(−6)2 \cdot \frac{1}{2}x = 2 \cdot (-6)

STEP 6

(This gives us:
x=−12x = -12

STEP 7

The x-intercept is \((-12, 0).

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