Q. Find the x-intercept of the line \(14x + 11y = -20\).

Q: How do I find the x-intercept of 14x+11y=-20?

Set y=0: 14x=-20. Solve x=-20/14, simplify to x=-10/7. The x-intercept is (-10/7,0).

Q: Can the fraction -20/14 be simplified?.

Yes, divide numerator and denominator by 2: -20/14 = -10/7 . That is the simplified exact value.

Q: What is the slope of the line 14x+11y=-20?

Solve for y: 11y = -14x - 20, so y = (-14/11)x - 20/11. The slope is -14/11.

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

Set x=0: 11y=-20, so y=-20/11. The y-intercept is (0,-20/11).

Q: Could a line have no x-intercept?

Only if the line is vertical of form x=c. Here the coefficient of x is nonzero, so this line does cross the x-axis and has an x-intercept.

Q: How can I check my x-intercept is correct?

Substitute (-10/7,0) into the equation: 14(-10/7)+11(0)=-20 gives -20=-20. Equality holds, so the intercept is correct.

Answer

When \(y=0\), \(14x+11\cdot0=-20\), so \(14x=-20\), \(x=-\tfrac{20}{14}=-\tfrac{10}{7}\). The x-intercept is \((-10/7,0)\).

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. In symbols, set \(y=0\).
Substitute \(y=0\) into the given equation:
Substitute into \(14x+11y=-20\) to get \(14x+11(0)=-20\).
Simplify the left side:
Compute \(11\cdot 0=0\), so the equation becomes \(14x+0=-20\), which simplifies to \(14x=-20\).
Isolate x by dividing both sides by 14:
Divide both sides by 14 to obtain \(x=\frac{-20}{14}\).
Simplify the fraction:
The greatest common divisor of 20 and 14 is 2, so divide numerator and denominator by 2 to get \(x=\frac{-10}{7}\).
State the x-intercept as a coordinate:
The x-intercept is \(\left(-\frac{10}{7},\,0\right)\).

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Algebra FAQs

What is an x-intercept?

The x-intercept is the point where a graph crosses the x-axis, so \(y=0\). It is written as \((x,0)\), the x-value where the line meets the axis.

How do I find the x-intercept of \(14x+11y=-20\)?

Set \(y=0\): \(14x=-20\). Solve \(x=-20/14\), simplify to \(x=-10/7\). The x-intercept is \((-10/7,0)\).

Can the fraction \(-20/14\) be simplified?.

Yes, divide numerator and denominator by 2: \( -20/14 = -10/7 \). That is the simplified exact value.

What is the slope of the line \(14x+11y=-20\)?

Solve for \(y\): \(11y = -14x - 20\), so \(y = (-14/11)x - 20/11\). The slope is \(-14/11\).

What is the y-intercept of the line?

Set \(x=0\): \(11y=-20\), so \(y=-20/11\). The y-intercept is \((0,-20/11)\).

How do I graph the line using intercepts?

Could a line have no \(x\)-intercept?

Only if the line is vertical of form \(x=c\). Here the coefficient of \(x\) is nonzero, so this line does cross the \(x\)-axis and has an \(x\)-intercept.

How can I check my x-intercept is correct?

Substitute \( (-10/7,0) \) into the equation: \(14(-10/7)+11(0)=-20\) gives \(-20=-20\). Equality holds, so the intercept is correct.

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