Q. find the x-intercept of the line 4x+11y=20.

Q: How do I find the x-intercept of 4x+11y=20?

Set y=0 and solve: 4x=20, so x=5. The x-intercept is the point (5,0).

Q: How do I find the y-intercept of 4x+11y=20?

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

Q: What is the slope of the line 4x+11y=20?

Rewrite as y=-\tfrac{4}{11}x+\tfrac{20}{11}. The slope is -\tfrac{4}{11}.

Q: How do I write the equation in slope-intercept form?

Solve for y: 11y=20-4x, so y=-\tfrac{4}{11}x+\tfrac{20}{11}.

Q: How do I write the equation in intercept form x/a+y/b=1?

Divide both sides by 20: \tfrac{4x}{20}+\tfrac{11y}{20}=1. So \tfrac{x}{5}+\tfrac{y}{20/11}=1, with intercepts a=5, b=\tfrac{20}{11}.

Q: How can I quickly check the x-intercept on a graph?

Plot the point (5,0) and verify it lies on the line by substituting into the equation: 4(5)+11(0)=20 holds, so the point is correct.

Q: What if the x-coefficient were zero, e.g., 0x+11y=20?

Then the line is horizontal: y=\tfrac{20}{11}. It has no x-intercept unless the constant were 0 (which would make the line the x- and y-origin).

Q: What happens to intercepts if the right-hand constant is 0, 4x+11y=0?

The line passes through the origin. Both intercepts are 0: x-intercept (0,0) and y-intercept (0,0).

Answer

Set \(y=0\). Then \(4x+11(0)=20\), so \(4x=20\) and \(x=5\). Hence the x-intercept is \((5,0)\).

Detailed Explanation

Problem

Find the x-intercept of the line given by the equation

4x + 11y = 20

Step-by-step explanation

Recall the definition of an x-intercept.

The x-intercept of a line is the point where the line crosses the x-axis. At any point on the x-axis the y-coordinate is 0. Therefore to find the x-intercept we set y equal to 0 in the equation of the line.
Substitute y = 0 into the equation.

\[4x + 11(0) = 20\]

Because y = 0, the term 11y becomes 11 · 0.
Simplify the equation.

\[4x + 0 = 20\]

\[4x = 20\]
Solve for x.

Divide both sides of the equation by 4 to isolate x.

\[x = \frac{20}{4}\]

\[x = 5\]
Write the x-intercept as a coordinate point and verify.

The x-intercept is the point with x = 5 and y = 0, so the x-intercept is

\[(5,\,0)\]

Verification by substitution: plug x = 5 and y = 0 into the original equation:

\[4(5) + 11(0) = 20\]

\[20 + 0 = 20\]

The left-hand side equals the right-hand side, so the solution is correct.

Answer

The x-intercept is (5, 0).

See full solution

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FAQs

How do I find the x-intercept of \(4x+11y=20\)?

Set \(y=0\) and solve: \(4x=20\), so \(x=5\). The x-intercept is the point \((5,0)\).

How do I find the y-intercept of \(4x+11y=20\)?

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

What is the slope of the line \(4x+11y=20\)?

Rewrite as \(y=-\tfrac{4}{11}x+\tfrac{20}{11}\). The slope is \(-\tfrac{4}{11}\).

How do I write the equation in slope-intercept form?

Solve for \(y\): \(11y=20-4x\), so \(y=-\tfrac{4}{11}x+\tfrac{20}{11}\).

How do I write the equation in intercept form \(x/a+y/b=1\)?

Divide both sides by 20: \(\tfrac{4x}{20}+\tfrac{11y}{20}=1\). So \(\tfrac{x}{5}+\tfrac{y}{20/11}=1\), with intercepts \(a=5\), \(b=\tfrac{20}{11}\).

How can I quickly check the x-intercept on a graph?

Plot the point \((5,0)\) and verify it lies on the line by substituting into the equation: \(4(5)+11(0)=20\) holds, so the point is correct.

What if the x-coefficient were zero, e.g., \(0x+11y=20\)?

Then the line is horizontal: \(y=\tfrac{20}{11}\). It has no x-intercept unless the constant were 0 (which would make the line the x- and y-origin).

What happens to intercepts if the right-hand constant is 0, \(4x+11y=0\)?

The line passes through the origin. Both intercepts are \(0\): x-intercept \((0,0)\) and y-intercept \((0,0)\).

To find the x-intercept, set y = 0.
Then solve for x.

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Q. find the x-intercept of the line 4x+11y=20.

Answer

Detailed Explanation

Problem

Step-by-step explanation

Answer

Graph

FAQs

How do I find the x-intercept of \(4x+11y=20\)?

How do I find the y-intercept of \(4x+11y=20\)?

What is the slope of the line \(4x+11y=20\)?

How do I write the equation in slope-intercept form?

How do I write the equation in intercept form \(x/a+y/b=1\)?

How can I quickly check the x-intercept on a graph?

What if the x-coefficient were zero, e.g., \(0x+11y=20\)?

What happens to intercepts if the right-hand constant is 0, \(4x+11y=0\)?

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