Q. Find the \(x\)-intercept of the line \(4x+11y=20\)
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
Graph
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 \(y = \frac{20}{11}\). The y-intercept is \(\left(0, \frac{20}{11}\right)\).
What is the slope of the line \(4x+11y=20\)?
Rewrite as \(y = -\frac{4}{11}x + \frac{20}{11}\). The slope is \(-\frac{4}{11}\).
How do I write the equation in slope-intercept form?
Solve for \(y\): \(11y = 20 - 4x\), so \(y = -\frac{4}{11}x + \frac{20}{11}\).
How do I write the equation in intercept form \(x/a+y/b=1\)?
Divide both sides by 20: \(\frac{4x}{20} + \frac{11y}{20} = 1\). So \(\frac{x}{5} + \frac{y}{20/11} = 1\), with intercepts \(a=5\), \(b=\frac{20}{11}\).
How can I quickly check the x-intercept on a graph?
How can I quickly check the x-intercept on a graph?
What if the x-coefficient were zero, e.g., \(0x+11y=20\)?
Then the line is horizontal: \(y=\frac{20}{11}\). 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.
Then solve for x.
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