Algebra Examples

$(4, 3)$ ; slope $\frac{1}{2}$

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.

$y = (\frac{1}{2}) x + b$

Step 1.3

Substitute the value of $x$ into the equation.

$y = (\frac{1}{2}) \cdot (4) + b$

Step 1.4

Substitute the value of $y$ into the equation.

$3 = (\frac{1}{2}) \cdot (4) + b$

Step 1.5

Find the value of $b$ .

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Step 1.5.1

Rewrite the equation as $\frac{1}{2} \cdot 4 + b = 3$ .

$\frac{1}{2} \cdot 4 + b = 3$

Step 1.5.2

Cancel the common factor of $2$ .

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Step 1.5.2.1

Factor $2$ out of $4$ .

$\frac{1}{2} \cdot (2 (2)) + b = 3$

Step 1.5.2.2

Cancel the common factor.

$\frac{1}{2} \cdot (2 \cdot 2) + b = 3$

Step 1.5.2.3

Rewrite the expression.

$2 + b = 3$

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 $2$ from both sides of the equation.

$b = 3 - 2$

Step 1.5.3.2

Subtract $2$ from $3$ .

$b = 1$

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.

$y = \frac{1}{2} x + 1$

Step 3