Q. Find the x-intercept of the line \( 18x – 5y = 12 \)

Answer

Set y to 0.\[ 18x – 5(0) = 12 \]
Solve for x.\[ 18x = 12 \]
\[ x = \frac{12}{18} \]
Simplify the fraction.\[ x = \frac{2}{3} \]
The x-intercept is (2/3, 0).

Detailed Explanation

Find the x-intercept of the line

We are given the equation of the line:

\[ 18x – 5y = 12 \]

Recall the definition of the x-intercept.The x-intercept is the point where the line crosses the x-axis. At any point on the x-axis the y-coordinate is 0. So to find the x-intercept set
\[ y = 0 \]
Substitute y = 0 into the equation.Replace y with 0 in the given equation:
\[ 18x – 5(0) = 12 \]

Simplify the left side because 5(0) = 0:

\[ 18x = 12 \]
Solve for x.Divide both sides of the equation by 18 to isolate x:
\[ x = \frac{12}{18} \]

Simplify the fraction by dividing numerator and denominator by their greatest common divisor, 6:

\[ x = \frac{12 \div 6}{18 \div 6} = \frac{2}{3} \]
Write the x-intercept as a point.The x-intercept has coordinates \[ x = \tfrac{2}{3} \] and \[ y = 0 \], so the x-intercept is the point
\[ \left(\tfrac{2}{3},\,0\right) \]

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Frequently Asked Questions

What is the x-intercept of 18x - 5y = 12?

Set y = 0: 18x = 12, so x = 12/18 = 2/3. The x-intercept point is (2/3, 0).

How do you find an x-intercept from any linear equation?

Set y = 0 and solve the resulting equation for x.

What is the y-intercept of 18x - 5y = 12?

Set x = 0: -5y = 12, so y = -12/5. The y-intercept point is (0, -12/5).

What is the slope of the line 18x - 5y = 12?

Rearrange to y = (18/5)x - 12/5, so the slope is 18/5 (or 3.6).

How can I graph this line quickly?

Plot the x-intercept (2/3, 0) and the y-intercept (0, -12/5), then draw the line through those two points.

How can I check that (2/3, 0) is correct?

Substitute x = 2/3 and y = 0 into 18x - 5y = 12: 18*(2/3) - 5*0 = 12, so it satisfies the equation.

Is there quick formulfor the x-intercept from Ax + By = C?

Yes: set y = 0 so x = C/(provided ≠ 0).

What if the x-intercept is fraction — how do I express it as decimal?

Convert 2/3 to decimal: 2/3 ≈ 0.666..., often rounded to 0.667 for three decimal places.

When does line have no x-intercept?

horizontal line y = k has no x-intercept when k ≠ 0. (If k = 0 the line is the x-axis and intersects everywhere.)

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