Q. find the slope of the line (y = \frac{3}{11}x + \frac{3}{16}).

Q: What is the slope of the line y = \frac{3}{11}x + \frac{3}{16} ?

The slope is the coefficient of x: m = \frac{3}{11}.

Q: How do you identify slope from slope-intercept form?

In y = mx + b the slope is m; the constant b is the y-intercept.

Q: What is the y-intercept of this line?

The y-intercept is b = \frac{3}{16}, i.e., the point (0,\tfrac{3}{16}).

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

Plot (0,\tfrac{3}{16}). From there use rise/run =\tfrac{3}{11}: go up 3 and right 11 (or down 3 and left 11) and draw the line through those points.

Q: How do I convert the slope to a decimal?

\frac{3}{11} \approx 0.272727\ldots (repeating).

Q: What is the slope of a line parallel to this one?

Any line parallel has the same slope: m = \frac{3}{11}.

Q: What is the slope of a line perpendicular to this one?

The perpendicular slope is the negative reciprocal: m_{\perp} = -\frac{11}{3}.

Q: How do I find the slope given two points on this line?

Use m = \frac{y_2-y_1}{x_2-x_1} . For any two points on this line that fraction will equal \frac{3}{11} .

Q: Does the fraction \frac{3}{11} simplify further?

No. 3 and 11 are coprime, so \frac{3}{11} is in simplest form.

Q: How do I find the x-intercept?

Set y=0 : 0=\tfrac{3}{11}x+\tfrac{3}{16}. Solve to get x = -\frac{11}{16}.

Answer

In slope-intercept form \(y = mx + b\), \(m\) is the slope. Here \(y = \frac{3}{11}x + \frac{3}{16}\), so the slope is \(\frac{3}{11}\).

Detailed Explanation

Solution — step by step

Step 1 — Recognize the slope-intercept form

What to do separately: Identify the general form of a line that reveals the slope directly.

The slope-intercept form of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
Step 2 — Write the given equation clearly as fractions

What to do separately: Rewrite the given expression so the coefficient of x is clearly a fraction.

The given equation is \(y = \tfrac{3}{11}x + \tfrac{3}{16}\).
Step 3 — Compare to the slope-intercept form and identify the slope

What to do separately: Match the coefficient of x in the given equation to m in \(y = mx + b\).

Comparing \(y = \tfrac{3}{11}x + \tfrac{3}{16}\) with \(y = mx + b\), the slope is \(m = \tfrac{3}{11}\).
Step 4 — (Optional) Decimal approximation

What to do separately: If a decimal is preferred, compute the approximate value.

\(\tfrac{3}{11} \approx 0.2727\ldots\)

Final answer: The slope is \(\tfrac{3}{11}\).

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FAQs

What is the slope of the line \( y = \frac{3}{11}x + \frac{3}{16} \)?

The slope is the coefficient of \(x\): \(m = \frac{3}{11}\).

How do you identify slope from slope-intercept form?

In \( y = mx + b \) the slope is \(m\); the constant \(b\) is the y-intercept.

What is the y-intercept of this line?

The y-intercept is \(b = \frac{3}{16}\), i.e., the point \((0,\tfrac{3}{16})\).

How do I graph the line using slope and intercept?

Plot \((0,\tfrac{3}{16})\). From there use rise/run \(=\tfrac{3}{11}\): go up 3 and right 11 (or down 3 and left 11) and draw the line through those points.

How do I convert the slope to a decimal?

\( \frac{3}{11} \approx 0.272727\ldots\) (repeating).

What is the slope of a line parallel to this one?

Any line parallel has the same slope: \(m = \frac{3}{11}\).

What is the slope of a line perpendicular to this one?

The perpendicular slope is the negative reciprocal: \(m_{\perp} = -\frac{11}{3}\).

How do I find the slope given two points on this line?

Use \( m = \frac{y_2-y_1}{x_2-x_1} \). For any two points on this line that fraction will equal \( \frac{3}{11} \).

Does the fraction \( \frac{3}{11} \) simplify further?

No. 3 and 11 are coprime, so \( \frac{3}{11} \) is in simplest form.

How do I find the x-intercept?

Set \( y=0 \): \(0=\tfrac{3}{11}x+\tfrac{3}{16}\). Solve to get \( x = -\frac{11}{16}\).

The slope is 3/11 for this line now.
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