Q. find the slope of the line (y = \frac{2}{9}x + \frac{6}{13}).

Q: What is the slope of y = \frac{2}{9}x + \frac{6}{13}?

The slope is the coefficient of x: m = \frac{2}{9}.

Q: What is the y-intercept of y = \frac{2}{9}x + \frac{6}{13}?

The y-intercept is the constant term: \left(0,\frac{6}{13}\right).

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

Solve for y: y = -\frac{A}{B}x + \frac{C}{B}. The slope is m = -\frac{A}{B}.

Q: How do you compute slope between two points (x_1,y_1) and (x_2,y_2)?

Use m = \frac{y_2 - y_1}{x_2 - x_1}, provided x_1 \ne x_2.

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

Parallel lines have m = \frac{2}{9}. Perpendicular lines have slope m = -\frac{9}{2} (the negative reciprocal).

Q: How do you graph y = \frac{2}{9}x + \frac{6}{13} quickly?

Plot the y-intercept \left(0,\frac{6}{13}\right), then use rise/run: rise 2, run 9 (or scale down) to mark another point and draw the line.

Q: Is \frac{2}{9} a repeating decimal and what is it approximately?

Yes, \frac{2}{9} \approx 0.\overline{2} (about 0.222...). Use the fraction for exact work.

Q: How can I tell if the line is increasing or decreasing?

Since m=\frac{2}{9}>0, the line is increasing: as x increases, y increases.

Answer

The line is \(y = \frac{2}{9}x + \frac{6}{13}\). In slope–intercept form \(y = mx + b\) the slope \(m\) is the coefficient of \(x\), so \(m = \frac{2}{9}\). Final result: slope = \(\frac{2}{9}\).

Detailed Explanation

Find the slope of the line

Recognize the slope-intercept form of a line. A linear equation in slope-intercept form is written as
\(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
Compare the given equation to the slope-intercept form. The given equation is
\(y = \tfrac{2}{9}x + \tfrac{6}{13}\).

Here the coefficient of \(x\) is \(\tfrac{2}{9}\), so that coefficient is the slope.
State the slope. The slope of the line is
\(\displaystyle m = \tfrac{2}{9}\).
Optional verification (using two points on the line). Evaluate the line at \(x=0\) to get the y-intercept:
\(y(0) = \tfrac{6}{13}\), giving point \((0,\tfrac{6}{13})\).

Evaluate the line at \(x=9\):
\(y(9) = \tfrac{2}{9}\cdot 9 + \tfrac{6}{13} = 2 + \tfrac{6}{13} = \tfrac{32}{13}\), giving point \((9,\tfrac{32}{13})\).

Compute the slope between these two points:
\(\dfrac{\tfrac{32}{13} – \tfrac{6}{13}}{9 – 0} = \dfrac{\tfrac{26}{13}}{9} = \dfrac{2}{9}\), which matches the coefficient found earlier.

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FAQs

What is the slope of \(y = \frac{2}{9}x + \frac{6}{13}\)?

The slope is the coefficient of \(x\): \(m = \frac{2}{9}\).

What is the y-intercept of \(y = \frac{2}{9}x + \frac{6}{13}\)?

The y-intercept is the constant term: \(\left(0,\frac{6}{13}\right)\).

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

Solve for \(y\): \(y = -\frac{A}{B}x + \frac{C}{B}\). The slope is \(m = -\frac{A}{B}\).

How do you compute slope between two points \((x_1,y_1)\) and \((x_2,y_2)\)?

Use \(m = \frac{y_2 - y_1}{x_2 - x_1}\), provided \(x_1 \ne x_2\).

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

Parallel lines have \(m = \frac{2}{9}\). Perpendicular lines have slope \(m = -\frac{9}{2}\) (the negative reciprocal).

How do you graph \(y = \frac{2}{9}x + \frac{6}{13}\) quickly?

Plot the y-intercept \(\left(0,\frac{6}{13}\right)\), then use rise/run: rise 2, run 9 (or scale down) to mark another point and draw the line.

Is \(\frac{2}{9}\) a repeating decimal and what is it approximately?

Yes, \(\frac{2}{9} \approx 0.\overline{2}\) (about 0.222...). Use the fraction for exact work.

How can I tell if the line is increasing or decreasing?

Since \(m=\frac{2}{9}>0\), the line is increasing: as \(x\) increases, \(y\) increases.

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