Q. Find the x-intercept of the line \(12x + 11y = 8\).

Q: What is the x-intercept of the line 12x+11y=8?

Set y=0. Then 12x=8, so x=\frac{8}{12}=\frac{2}{3}. The x-intercept is \left(\frac{2}{3},0\right).

Q: How do you find an x-intercept in general from ax+by=c?

Set y=0. Solve ax = c, so x = \frac{c}{a}. For this line x = \frac{8}{12} = \frac{2}{3}.

Q: What is the y-intercept of this line?

Set x=0. Then 11y=8, so y=\frac{8}{11}. The y-intercept is \left(0, \frac{8}{11}\right).

Q: What is the slope of the line?

Rewrite as y = -\frac{12}{11}x + \frac{8}{11}. The slope is -\frac{12}{11}.

Q: How can I graph the line quickly?

Plot the intercepts \left(\frac{2}{3}, 0\right) and \left(0, \frac{8}{11}\right). Draw the straight line through those two points.

Q: How do I check the intercept is correct?

Substitute \left(\frac{2}{3}, 0\right) into 12x+11y: 12 \cdot \frac{2}{3} + 11 \cdot 0 = 8. Since 8=8, it is correct.

Q: How to write the equation in intercept form?

Intercept form is \frac{x}{a} + \frac{y}{b} = 1. Here a = \frac{2}{3}, b = \frac{8}{11}, so \frac{x}{2/3} + \frac{y}{8/11} = 1.

Answer

Set \(y=0\): \(12x+11(0)=8\), so \(12x=8\) and \(x=\dfrac{8}{12}=\dfrac{2}{3}\).
x-intercept: \(\left(\dfrac{2}{3},\,0\right)\).

Detailed Explanation

Understand the x-intercept: it is the point where the line crosses the x-axis, so the y-coordinate is 0. The x-intercept has the form \( (x,0) \).
Start with the given equation of the line: \(12x + 11y = 8\). Substitute \(y = 0\) because we are finding where the line meets the x-axis: \(12x + 11\cdot 0 = 8\).
Simplify the equation after substitution: \(12x = 8\).
Solve for \(x\) by dividing both sides by 12: \(x = \dfrac{8}{12}\).
Reduce the fraction by dividing numerator and denominator by 4: \(x = \dfrac{2}{3}\).
Therefore, the x-intercept is \( \left(\dfrac{2}{3},\,0\right) \).

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FAQs

What is the x-intercept of the line \(12x+11y=8\)?

Set \(y=0\). Then \(12x=8\), so \(x=\frac{8}{12}=\frac{2}{3}\). The x-intercept is \(\left(\frac{2}{3},0\right)\).

How do you find an x-intercept in general from \(ax+by=c\)?

Set \(y=0\). Solve \(ax = c\), so \(x = \frac{c}{a}\). For this line \(x = \frac{8}{12} = \frac{2}{3}\).

What is the y-intercept of this line?

Set \(x=0\). Then \(11y=8\), so \(y=\frac{8}{11}\). The y-intercept is \(\left(0, \frac{8}{11}\right)\).

What is the slope of the line?

Rewrite as \(y = -\frac{12}{11}x + \frac{8}{11}\). The slope is \(-\frac{12}{11}\).

How can I graph the line quickly?

Plot the intercepts \(\left(\frac{2}{3}, 0\right)\) and \(\left(0, \frac{8}{11}\right)\). Draw the straight line through those two points.

What is the x-intercept as a decimal?

How do I check the intercept is correct?

Substitute \(\left(\frac{2}{3}, 0\right)\) into \(12x+11y\): \(12 \cdot \frac{2}{3} + 11 \cdot 0 = 8\). Since \(8=8\), it is correct.

How to write the equation in intercept form?

Intercept form is \(\frac{x}{a} + \frac{y}{b} = 1\). Here \(a = \frac{2}{3}\), \(b = \frac{8}{11}\), so \(\frac{x}{2/3} + \frac{y}{8/11} = 1\).

Set y = 0 and solve for x: x = 2/3.
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