Algebra Examples

What is the equation of the line that has a slope of $\frac{1}{3}$ and goes through the point $(3, 1)$ ?

Step 1

Find the value of $b$ using the formula for the equation of a line.

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Step 1.1

Use the formula for the equation of a line to find $b$ .

$y = m x + b$

Step 1.2

Substitute the value of $m$ into the equation.

$y = (\frac{1}{3}) x + b$

Step 1.3

Substitute the value of $x$ into the equation.

$y = (\frac{1}{3}) \cdot (3) + b$

Step 1.4

Substitute the value of $y$ into the equation.

$1 = (\frac{1}{3}) \cdot (3) + b$

Step 1.5

Find the value of $b$ .

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Step 1.5.1

Rewrite the equation as $\frac{1}{3} \cdot 3 + b = 1$ .

$\frac{1}{3} \cdot 3 + b = 1$

Step 1.5.2

Cancel the common factor of $3$ .

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Step 1.5.2.1

Cancel the common factor.

$\frac{1}{3} \cdot 3 + b = 1$

Step 1.5.2.2

Rewrite the expression.

$1 + b = 1$

Step 1.5.3

Move all terms not containing $b$ to the right side of the equation.

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Step 1.5.3.1

Subtract $1$ from both sides of the equation.

$b = 1 - 1$

Step 1.5.3.2

Subtract $1$ from $1$ .

$b = 0$

Step 2

Now that the values of $m$ (slope) and $b$ (y-intercept) are known, substitute them into $y = m x + b$ to find the equation of the line.

$y = \frac{1}{3} x$

Step 3