Q. Find the y-intercept of the line \(15x + 18y = -20\).

Q: How do I find the y-intercept of the line 15x+18y=-20?.

Set x=0. Then 18y=-20, so y=-\tfrac{10}{9}. The y-intercept point is (0,-\tfrac{10}{9}).

Q: What is the slope of this line?

Solve for y: y=-\tfrac{5}{6}x-\tfrac{10}{9}. The slope is -\tfrac{5}{6}.

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

Set y=0. Then 15x=-20, so x=-\tfrac{4}{3}. The x-intercept is (-\tfrac{4}{3},0).

Q: How can I graph the line quickly?

Plot the intercepts (0,-\tfrac{10}{9}) and (-\tfrac{4}{3},0) , then draw the line through them; or use slope -\tfrac{5}{6} from the y-intercept: down 5, right 6.

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

Rearrange: y=-\tfrac{5}{6}x-\tfrac{10}{9}.

Q: What is the y-intercept as a decimal?

What is the y-intercept as a decimal?

Answer

Set x=0: \(18y=-20\), so \(y=-20/18=-10/9\). Thus the y-intercept is \((0,-10/9)\).

Detailed Explanation

Step 1 — What the y-intercept means

The y-intercept is the point where the line crosses the y-axis, so the x-coordinate is 0. Therefore set \(x = 0\).

Step 2 — Substitute x = 0 into the equation

Start from the given equation:

\[15x + 18y = -20\]

Substitute \(x = 0\):

\[15(0) + 18y = -20\]

Compute \(15(0) = 0\) to get:

\[0 + 18y = -20\]

\[18y = -20\]

Step 3 — Solve for y

Divide both sides by 18 to isolate \(y\):

\[y = \frac{-20}{18}\]

Reduce the fraction by dividing numerator and denominator by 2:

\[y = \frac{-10}{9}\]

Step 4 — State the y-intercept

The y-intercept is the point on the y-axis corresponding to this y-value:

\[(0, -\tfrac{10}{9})\]

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Algebra FAQs

How do I find the y-intercept of the line \(15x+18y=-20\)?.

Set \(x=0\). Then \(18y=-20\), so \(y=-\tfrac{10}{9}\). The y-intercept point is \((0,-\tfrac{10}{9})\).

What is the slope of this line?

Solve for \(y\): \(y=-\tfrac{5}{6}x-\tfrac{10}{9}\). The slope is \(-\tfrac{5}{6}\).

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

Set \(y=0\). Then \(15x=-20\), so \(x=-\tfrac{4}{3}\). The x-intercept is \((-\tfrac{4}{3},0)\).

How can I graph the line quickly?

Plot the intercepts \( (0,-\tfrac{10}{9}) \) and \( (-\tfrac{4}{3},0) \), then draw the line through them; or use slope \(-\tfrac{5}{6}\) from the y-intercept: down 5, right 6.

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

Rearrange: \(y=-\tfrac{5}{6}x-\tfrac{10}{9}\).

What is the \(y\)-intercept as a decimal?

Can the intercepts be simplified or scaled for nicer integers?

Multiply by a common factor: for example, scaling both coordinates by 9 gives y-intercept \( (0,-10) \) in scaled units, but the true intercept remains \( (0,-\tfrac{10}{9}) \).

Why is setting \(x=0\) the correct method for y-intercept?

The y-intercept is where the line crosses the y-axis, and every point on the y-axis has \(x=0\); solving with \(x=0\) gives the y-coordinate of that crossing.

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