Q. Find the y-intercept of the line \(y = -\frac{9}{13}x – \frac{11}{8}\).

Q: What is the y-intercept of the line y = -\tfrac{9}{13}x - \tfrac{11}{8}?

The y-intercept is y = -\tfrac{11}{8}, i.e. the point (0,\,-\tfrac{11}{8}).

Q: How do you find a y-intercept from slope-intercept form?

Set x=0 and evaluate y. For y=-\tfrac{9}{13}x-\tfrac{11}{8}, y(0)=-\tfrac{11}{8}.

Q: What is the slope of the line?

The slope is the coefficient of x: -\tfrac{9}{13} (rise/run = -\tfrac{9}{13}).

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

Decimal: (-1.375). Mixed number: (-1\tfrac{3}{8})..

Q: How do I graph the line using the y-intercept and slope?

Plot 0,-\tfrac{11}{8}. From there, use slope -\tfrac{9}{13}: go right 13, down 9 (or left 13, up 9), then draw the line through those points..

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

What is the x-intercept of the line?

Q: How do I write the equation in standard form Ax + By + C = 0?

Rearranged and cleared of fractions: 72x + 104y + 143 = 0.

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

Use intercepts a=\tfrac{143}{72}, b=-\tfrac{11}{8}: \[\dfrac{x}{\tfrac{143}{72}} + \dfrac{y}{-\tfrac{11}{8}} = 1.\]

Q: Why is the y-intercept useful?

It shows where the line crosses the y-axis, gives an initial point for graphing, and helps convert or compare forms of the line equation.

Answer

Set \(x=0\).

Then \(y=-\frac{11}{8}\).

Thus, the \(y\)-intercept is \(\left(0,-\frac{11}{8}\right)\).

Detailed Explanation

Understand what the y-intercept is: the y-intercept is the point where the graph crosses the y-axis, which occurs when the x-coordinate equals 0. So set \(x = 0\).
Write the given line and substitute \(x = 0\):
\(y = -\frac{9}{13}x – \frac{11}{8}\)

Substitute \(x = 0\):

\(y = -\frac{9}{13}\cdot 0 – \frac{11}{8}\)
Compute each term:
\(-\frac{9}{13}\cdot 0 = 0\)

So \(y = 0 – \frac{11}{8} = -\frac{11}{8}\).
State the y-intercept as a point:
The y-intercept is \(\left(0,\; -\frac{11}{8}\right)\). In decimal form this is \(\left(0,\; -1.375\right)\).

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Algebra FAQs

What is the y-intercept of the line \(y = -\tfrac{9}{13}x - \tfrac{11}{8}\)?

The y-intercept is \(y = -\tfrac{11}{8}\), i.e. the point \((0,\,-\tfrac{11}{8})\).

How do you find a y-intercept from slope-intercept form?

Set \(x=0\) and evaluate \(y\). For \(y=-\tfrac{9}{13}x-\tfrac{11}{8}\), \(y(0)=-\tfrac{11}{8}\).

What is the slope of the line?

The slope is the coefficient of \(x\): \(-\tfrac{9}{13}\) (rise/run = \(-\tfrac{9}{13}\)).

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

Decimal: \((-1.375)\). Mixed number: \((-1\tfrac{3}{8})\)..

How do I graph the line using the \(y\)-intercept and slope?

Plot \(0,-\tfrac{11}{8}\). From there, use slope \(-\tfrac{9}{13}\): go right \(13\), down \(9\) (or left \(13\), up \(9\)), then draw the line through those points..

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

How do I write the equation in standard form \(Ax + By + C = 0\)?

Rearranged and cleared of fractions: \(72x + 104y + 143 = 0\).

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

Use intercepts \(a=\tfrac{143}{72}\), \(b=-\tfrac{11}{8}\): \[\dfrac{x}{\tfrac{143}{72}} + \dfrac{y}{-\tfrac{11}{8}} = 1.\]

Why is the \(y\)-intercept useful?

It shows where the line crosses the \(y\)-axis, gives an initial point for graphing, and helps convert or compare forms of the line equation.

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