Q. find the x-intercept of the line 5x + 18y = 4.

Q: How do you find the x-intercept of 5x+18y=4?

Set y=0. Solve 5x=4 so x=\tfrac{4}{5}. The x-intercept is (\tfrac{4}{5},0).

Q: What is the y-intercept of 5x+18y=4?

Set x=0. Solve 18y=4 so y=\tfrac{2}{9}. The y-intercept is (0,\tfrac{2}{9}).

Q: How do you convert 5x+18y=4 to slope-intercept form?

Solve for y: 18y=4-5x so y=-\tfrac{5}{18}x+\tfrac{2}{9}.

Q: What is the slope of the line 5x+18y=4?

From slope-intercept form, the slope is m=-\tfrac{5}{18}.

Q: How can I check my x-intercept calculation?

Substitute (\tfrac{4}{5},0) into the equation: 5(\tfrac{4}{5})+18(0)=4 gives 4=4, so it checks.

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

Divide both sides by 4: \tfrac{5x}{4}+\tfrac{18y}{4}=1. This is x/(\tfrac{4}{5})+y/(\tfrac{2}{9})=1, so intercepts are a=\tfrac{4}{5}, b=\tfrac{2}{9}.

Q: How would I graph this line quickly?

Plot the intercepts (\tfrac{4}{5},0) and (0,\tfrac{2}{9}), then draw the straight line through them.

Q: What if the coefficient of y were zero?

Then the equation would be 5x=4, a vertical line x=\tfrac{4}{5}. It has an x-intercept at (\tfrac{4}{5},0) but no finite y-intercept unless x=0.

Answer

see the next answer here to check Set y=0: \(5x+18\cdot 0=4\) so \(5x=4\) and \(x=\tfrac{4}{5}\). The x-intercept is \(\left(\tfrac{4}{5},0\right)\).

Detailed Explanation

Problem

Find the x-intercept of the line given by the equation \(5x + 18y = 4\).

Explanation and step-by-step solution

Recall the definition of an x-intercept.

The x-intercept is the point where the graph of 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 \(y = 0\) in the equation of the line.
Substitute \(y = 0\) into the equation.

Starting from the given equation, substitute \(y = 0\):

\[5x + 18\cdot 0 = 4\]
Simplify the equation after substitution.

Evaluate the product \(18\cdot 0\):

\[5x + 0 = 4\]

Which simplifies to

\[5x = 4\]
Solve for \(x\).

Divide both sides of the equation by 5 to isolate \(x\):

\[x = \frac{4}{5}\]

Optionally, express as a decimal:

\[x = 0.8\]
Write the x-intercept as a coordinate point.

The x-intercept is the point on the x-axis with this x-coordinate and y = 0, so the x-intercept is

\[\left(\frac{4}{5},\,0\right)\]
Quick check (optional but instructive).

Substitute the point \(\left(\frac{4}{5},0\right)\) into the original equation to verify:

\[5\left(\frac{4}{5}\right) + 18(0) = 4 + 0 = 4\]

Since the left-hand side equals the right-hand side, the point is correct.

Final answer

The x-intercept is \(\left(\frac{4}{5},0\right)\) (which is \((0.8,0)\)).

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FAQs

How do you find the x-intercept of \(5x+18y=4\)?

Set \(y=0\). Solve \(5x=4\) so \(x=\tfrac{4}{5}\). The x-intercept is \((\tfrac{4}{5},0)\).

What is the y-intercept of \(5x+18y=4\)?

Set \(x=0\). Solve \(18y=4\) so \(y=\tfrac{2}{9}\). The y-intercept is \((0,\tfrac{2}{9})\).

How do you convert \(5x+18y=4\) to slope-intercept form?

Solve for \(y\): \(18y=4-5x\) so \(y=-\tfrac{5}{18}x+\tfrac{2}{9}\).

What is the slope of the line \(5x+18y=4\)?

From slope-intercept form, the slope is \(m=-\tfrac{5}{18}\).

How can I check my x-intercept calculation?

Substitute \((\tfrac{4}{5},0)\) into the equation: \(5(\tfrac{4}{5})+18(0)=4\) gives \(4=4\), so it checks.

How do I write the equation in intercept form?

Divide both sides by \(4\): \(\tfrac{5x}{4}+\tfrac{18y}{4}=1\). This is \(x/(\tfrac{4}{5})+y/(\tfrac{2}{9})=1\), so intercepts are \(a=\tfrac{4}{5}\), \(b=\tfrac{2}{9}\).

How would I graph this line quickly?

Plot the intercepts \((\tfrac{4}{5},0)\) and \((0,\tfrac{2}{9})\), then draw the straight line through them.

What if the coefficient of \(y\) were zero?

Then the equation would be \(5x=4\), a vertical line \(x=\tfrac{4}{5}\). It has an x-intercept at \((\tfrac{4}{5},0)\) but no finite y-intercept unless \(x=0\).

Set y = 0, then read the x-intercept.
Use y = 0 to solve for x.

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