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A line has a slope of $\frac{1}{3}$ and a $y$ -intercept of $-\frac{2}{3}$ . Write its equation in slope-intercept form. Write your answer using integers, proper fractions, and improper fractions in simplest form.

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Slope-intercept form: write an equation

Full solution

Q. A line has a slope of

\frac{1}{3}

and a

y

-intercept of

-\frac{2}{3}

. Write its equation in slope-intercept form. Write your answer using integers, proper fractions, and improper fractions in simplest form.

Identify Linear Equation Form: Identify the slope-intercept form of a linear equation. $\newline$ The slope-intercept form of a linear equation is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.
Insert Given Values: Insert the given slope and y-intercept into the slope-intercept form. $\newline$ We are given the slope $m$ as $\frac{1}{3}$ and the y-intercept $b$ as $-\frac{2}{3}$ . Substituting these values into the slope-intercept form, we get $y = \left(\frac{1}{3}\right)x + \left(-\frac{2}{3}\right)$ .
Simplify Equation: Simplify the equation if necessary. $\newline$ The equation $y = \frac{1}{3}x + \left(-\frac{2}{3}\right)$ is already in its simplest form, so no further simplification is needed.

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