Q. Find the y-intercept of the line \(y = \frac{5}{6}x + 5\).

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

In y = mx + b, the y-intercept is the constant term b. Set x=0 to get y=b.

Q: How do you find the y-intercept from standard form Ax + By = C?

Set x=0 and solve for y: By = C so y = \frac{C}{B}. The intercept point is (0, \frac{C}{B}).

Q: How would you graph y = \frac{5}{6}x + 5?

Plot the y-intercept (0,5). Use the slope m = \frac{5}{6}: from (0,5) go up 5 and right 6 to another point, then draw the line through them.

Q: How do you write the equation of a line given slope and y-intercept?

Use y = mx + b, where m is slope and b is the y-intercept. For example, slope \frac{5}{6} and intercept 5 gives y = \frac{5}{6}x + 5.

Q: How can I check my y-intercept quickly?

Substitute x=0 into the equation: the resulting y-value is the y-intercept. For y = \frac{5}{6}x + 5, plug x=0 to get y=5.

Answer

Set \(x=0\): \(y=\frac{5}{6}\cdot 0 + 5 = 5\). Thus the y-intercept is \((0,5)\).

Detailed Explanation

Step-by-step solution

Recognize the form of the line. The equation is

\[ y = \frac{5}{6}x + 5 \]

This is in slope-intercept form \( y = mx + b \), where \( b \) is the y-intercept (the value of \( y \) when \( x = 0 \)).
Find the y-coordinate where the line crosses the y-axis by setting \( x = 0 \):

\[ y = \frac{5}{6}\cdot 0 + 5 \]

Compute the product: \( \frac{5}{6}\cdot 0 = 0 \), so

\[ y = 0 + 5 = 5 \]
State the y-intercept. The line crosses the y-axis at the point

\[ (0,\,5) \]

The y-intercept value is \( 5 \).

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FAQs

What is the y-intercept of the line \(y = \frac{5}{6}x + 5\)?

The y-intercept is the value of y when x = 0, so y = 5. As a point: \((0,5)\).

What does "y-intercept" mean?

The y-intercept is where the graph crosses the y-axis, i.e., the point with \(x = 0\). In slope-intercept form \(y = mx + b\), the intercept is \((0, b)\).

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

In \(y = mx + b\), the y-intercept is the constant term \(b\). Set \(x=0\) to get \(y=b\).

How do you find the y-intercept from standard form \(Ax + By = C\)?

Set \(x=0\) and solve for \(y\): \(By = C\) so \(y = \frac{C}{B}\). The intercept point is \((0, \frac{C}{B})\).

How would you graph \(y = \frac{5}{6}x + 5\)?

Plot the y-intercept \((0,5)\). Use the slope \(m = \frac{5}{6}\): from \((0,5)\) go up 5 and right 6 to another point, then draw the line through them.

How do you find the x-intercept of the same line?

How do you write the equation of a line given slope and y-intercept?

Use \(y = mx + b\), where \(m\) is slope and \(b\) is the y-intercept. For example, slope \(\frac{5}{6}\) and intercept 5 gives \(y = \frac{5}{6}x + 5\).

How can I check my y-intercept quickly?

Substitute \(x=0\) into the equation: the resulting y-value is the y-intercept. For \(y = \frac{5}{6}x + 5\), plug \(x=0\) to get \(y=5\).

Evaluate the line at x = 0 to get 5.
The y-intercept is 5.

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