Q. Find the x-intercept of the line \(12x + 19y = 11\)

Q: What is the x-intercept of the line 12x+19y=11?.

Set y=0: 12x+19(0)=11 so 12x=11 and x=\frac{11}{12}. The x-intercept point is \left(\frac{11}{12},0\right)..

Q: How do I get the decimal value of the x-intercept?

Compute \frac{11}{12} = 0.916\overline{6} , about 0.9167 rounded to four decimal places.

Q: How do you find an x-intercept from standard form Ax+By=C?

Set y=0 and solve Ax=C. If A\neq 0 the x-intercept is \left(\frac{C}{A},0\right).

Q: What if A=0 in Ax+By=C?

If A=0 the equation is By=C. If C=0 the whole x-axis is a solution (every x-intercept); if C\neq 0 there is no x-intercept because y is a nonzero constant.

Q: How can I graph the line using intercepts?

Find x-intercept \left(\frac{11}{12},0\right) and y-intercept by setting x=0: y=\frac{11}{19}. Plot \left(\frac{11}{12},0\right) and \left(0,\frac{11}{19}\right), then draw the line through them.

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

What is the y-intercept of the same line?

Q: Can I write the line in slope-intercept form?

Yes. Solve for y: 19y=11-12x so y=-\frac{12}{19}x+\frac{11}{19}. The slope is -\frac{12}{19}..

Q: Is the x-intercept rational or irrational?

It is rational: x=\frac{11}{12} is a ratio of integers, hence rational.

Answer

Set \(y=0\): \(12x+19\cdot0=11\) so \(12x=11\), \(x=\tfrac{11}{12}\).
x-intercept: \((\tfrac{11}{12},0)\)

Detailed Explanation

Understand what an x-intercept is.The x-intercept is the point where the graph crosses the x-axis, so the y-coordinate is 0. Therefore to find the x-intercept of the line given by the equation, set y equal to 0.
Substitute y = 0 into the equation.Start with the line equation:
\[12x + 19y = 11\]

Replace y with 0:

\[12x + 19\cdot 0 = 11\]
Simplify the substituted equation.Multiply out and simplify the left side:
\[12x + 0 = 11\]

\[12x = 11\]
Solve for x.Divide both sides of the equation by 12 to isolate x:
\[x = \frac{11}{12}\]
Write the x-intercept as an ordered pair.The x-intercept is the point on the x-axis where x = 11/12 and y = 0, so the intercept is
\[\left(\frac{11}{12},\,0\right)\]

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Algebra FAQs

What is the x-intercept of the line \(12x+19y=11\)?.

Set \(y=0\): \(12x+19(0)=11\) so \(12x=11\) and \(x=\frac{11}{12}\). The \(x\)-intercept point is \(\left(\frac{11}{12},0\right)\)..

How do I get the decimal value of the \(x\)-intercept?

Compute \( \frac{11}{12} = 0.916\overline{6} \), about \( 0.9167 \) rounded to four decimal places.

How do you find an x-intercept from standard form \(Ax+By=C\)?

Set \(y=0\) and solve \(Ax=C\). If \(A\neq 0\) the \(x\)-intercept is \(\left(\frac{C}{A},0\right)\).

What if \(A=0\) in \(Ax+By=C\)?

If \(A=0\) the equation is \(By=C\). If \(C=0\) the whole \(x\)-axis is a solution (every \(x\)-intercept); if \(C\neq 0\) there is no \(x\)-intercept because \(y\) is a nonzero constant.

How can I graph the line using intercepts?

Find x-intercept \(\left(\frac{11}{12},0\right)\) and y-intercept by setting \(x=0\): \(y=\frac{11}{19}\). Plot \(\left(\frac{11}{12},0\right)\) and \(\left(0,\frac{11}{19}\right)\), then draw the line through them.

What is the \(y\)-intercept of the same line?

Can I write the line in slope-intercept form?

Yes. Solve for \(y\): \(19y=11-12x\) so \(y=-\frac{12}{19}x+\frac{11}{19}\). The slope is \(-\frac{12}{19}\)..

Is the \(x\)-intercept rational or irrational?

It is rational: \(x=\frac{11}{12}\) is a ratio of integers, hence rational.

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