Q. Find the y-intercept of the line \( y=2x + \frac{2}{13} \).

Q: What is the y-intercept of y=2x+\tfrac{2}{13}?

Set x=0: y=\tfrac{2}{13}. The y-intercept is the point (0,\tfrac{2}{13}).

Q: Why do we set x=0 to find the y-intercept?

The y-axis is the line x=0; the intersection with the given line occurs where x=0, so substituting x=0 yields the y-intercept.

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

In y=mx+b, the y-intercept is b. It is the point (0,b).

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

Set x=0. Then By=C so y=\tfrac{C}{B} (provided B\neq0), giving (0,\tfrac{C}{B}).

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

Set y=0: 0=2x+\tfrac{2}{13} so x=-\tfrac{1}{13}. The x-intercept is (-\tfrac{1}{13},0).

Q: How can you quickly graph the line using intercept and slope?

Plot the y-intercept (0,\tfrac{2}{13}). Use slope 2 (rise 2, run 1) to mark a second point, then draw the straight line through them.

Q: What if the original looks like y=2x+213 instead of +\tfrac{2}{13}?

If y=2x+213, the y-intercept is 213, point (0,213). Always confirm the intended constant.

Answer

see the next answer here to check Set x=0: \(y=2(0)+\frac{2}{13}=\frac{2}{13}\).
Thus the y-intercept is \(\left(0,\frac{2}{13}\right)\).

Detailed Explanation

Find the y-intercept of the line ( \( y = 2x + \dfrac{2}{13} \) )

Step 1 – Understand the definition of a y-intercept:

The y-intercept of a graph is the point where the line crosses the vertical y-axis. On the coordinate plane, every point on the y-axis has an x-coordinate of 0. Therefore, to find the y-intercept of any linear equation, you must substitute 0 for x and solve for y.
Step 2 – Identify the equation form:

The given equation is \( y = 2x + \dfrac{2}{13} \). This is written in slope-intercept form, which is generally expressed as:

\( y = mx + b \)

In this form, \( m \) represents the slope and \( b \) represents the y-intercept value.
Step 3 – Substitute 0 for x:

Plug \( x = 0 \) into the equation to find the corresponding y-value:

\( y = 2(0) + \dfrac{2}{13} \)
Step 4 – Simplify the expression:

Multiplying any number by 0 results in 0:

\( y = 0 + \dfrac{2}{13} \)

\( y = \dfrac{2}{13} \)
Final Answer:

The y-intercept is \( \dfrac{2}{13} \). As a coordinate point, this is represented as \( (0, \dfrac{2}{13}) \).

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FAQs

What is the y-intercept of \(y=2x+\tfrac{2}{13}\)?

Set \(x=0\): \(y=\tfrac{2}{13}\). The y-intercept is the point \((0,\tfrac{2}{13})\).

Why do we set \(x=0\) to find the y-intercept?

The y-axis is the line \(x=0\); the intersection with the given line occurs where \(x=0\), so substituting \(x=0\) yields the y-intercept.

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

In \(y=mx+b\), the y-intercept is \(b\). It is the point \((0,b)\).

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

Set \(x=0\). Then \(By=C\) so \(y=\tfrac{C}{B}\) (provided \(B\neq0\)), giving \((0,\tfrac{C}{B})\).

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

Set \(y=0\): \(0=2x+\tfrac{2}{13}\) so \(x=-\tfrac{1}{13}\). The x-intercept is \((-\tfrac{1}{13},0)\).

How can you quickly graph the line using intercept and slope?

Plot the y-intercept \((0,\tfrac{2}{13})\). Use slope \(2\) (rise 2, run 1) to mark a second point, then draw the straight line through them.

What if the original looks like \(y=2x+213\) instead of \(+\tfrac{2}{13}\)?

If \(y=2x+213\), the y-intercept is \(213\), point \((0,213)\). Always confirm the intended constant.

What common mistakes should I avoid when finding intercepts?

Don’t confuse slope and intercept, forget to set the correct variable to zero, or misread fractions/spacing. Always plug \(x=0\) for y-intercept and \(y=0\) for x-intercept and simplify carefully.

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