Q. Find the y-intercept of the line \(18x – y = 5\).

Q: How do I find the y-intercept from 18x - y = 5?.

Set x=0 and solve: 18(0)-y=5 gives y=-5. The y-intercept point is (0,-5).

Q: What is the slope of the line?

From y=18x-5 the slope is m=18.

Q: What is the x-intercept of the line?.

Set y=0: 18x=5 so x=\tfrac{5}{18}. The x-intercept point is \left(\tfrac{5}{18},0\right).

Q: How can I quickly graph this line?

Plot the y-intercept 0,-5 and another point like x=1 gives y=13, so plot 1,13. Draw the line through them (rise 18, run 1).

Q: How do I find the y-intercept directly from Ax + By = C?

How do I find the y-intercept directly from Ax + By = C?

Q: How can I check my answer is correct?

Substitute (0,-5) into the original equation: 18(0)-(-5)=5 gives 5=5. The point satisfies the equation, so it's correct.

Answer

Set x=0: \[18(0)-y=5,\ -y=5,\ y=-5.\]
Y-intercept: \[(0,-5)\]

Detailed Explanation

Find the y-intercept of the line 18x–y=5

Recall the definition of the y-intercept.The y-intercept is the point at which the graph of the line crosses the y-axis. At any point on the y-axis the x-coordinate is 0, so to find the y-intercept we set x = 0 in the equation of the line.
Substitute x = 0 into the equation.Start with the given equation:
\(18x – y = 5\)

Substitute \(x = 0\):

\(18(0) – y = 5\).
Simplify the left-hand side.Compute \(18(0)\):
\(0 – y = 5\),
which simplifies to

\(-y = 5\).
Solve for y.Multiply both sides of the equation \(-y = 5\) by \(-1\) to isolate y:
\(y = -5\).
State the y-intercept.The y-intercept point is \((0, -5)\). The y-intercept value (the y-coordinate where the line crosses the y-axis) is \(-5\).

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Algebra FAQs

How do I find the y-intercept from \(18x - y = 5\)?.

Set x=0 and solve: \(18(0)-y=5\) gives \(y=-5\). The y-intercept point is \((0,-5)\).

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

What is the slope of the line?

From \(y=18x-5\) the slope is \(m=18\).

What is the \(x\)-intercept of the line?.

Set \(y=0\): \(18x=5\) so \(x=\tfrac{5}{18}\). The x-intercept point is \(\left(\tfrac{5}{18},0\right)\).

How can I quickly graph this line?

Plot the y-intercept \(0,-5\) and another point like \(x=1\) gives \(y=13\), so plot \(1,13\). Draw the line through them (rise 18, run 1).

How do I find the y-intercept directly from \(Ax + By = C\)?

What does a negative \(y\)-intercept mean?

It means the line crosses the y-axis below the origin; here it crosses at \(y=-5\), so the point is \((0,-5)\).

How can I check my answer is correct?

Substitute \( (0,-5) \) into the original equation: \(18(0)-(-5)=5\) gives \(5=5\). The point satisfies the equation, so it's correct.

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