Algebra Examples

What is the equation of the line that passes through the point $(4, 4)$ and has a slope of $3$ ?

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.

$y = (3) \cdot x + b$

Step 1.3

Substitute the value of $x$ into the equation.

$y = (3) \cdot (4) + b$

Step 1.4

Substitute the value of $y$ into the equation.

$4 = (3) \cdot (4) + b$

Step 1.5

Find the value of $b$ .

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Step 1.5.1

Rewrite the equation as $(3) \cdot (4) + b = 4$ .

$(3) \cdot (4) + b = 4$

Step 1.5.2

Multiply $3$ by $4$ .

$12 + b = 4$

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 $12$ from both sides of the equation.

$b = 4 - 12$

Step 1.5.3.2

Subtract $12$ from $4$ .

$b = - 8$

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.

$y = 3 x - 8$

Step 3