Precalculus Examples

vertex $(4, 4)$ , point $(0, 0)$

Step 1

Use $y = m x + b$ to calculate the equation of the line, where $m$ represents the slope and $b$ represents the y-intercept.

To calculate the equation of the line, use the $y = m x + b$ format.

Step 2

Slope is equal to the change in $y$ over the change in $x$ , or rise over run.

$m = \frac{(change in y)}{(change in x)}$

Step 3

The change in $x$ is equal to the difference in x-coordinates (also called run), and the change in $y$ is equal to the difference in y-coordinates (also called rise).

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

Step 4

Substitute in the values of $x$ and $y$ into the equation to find the slope.

$m = \frac{0 - (4)}{0 - (4)}$

Step 5

Cancel the common factor of $0 - (4)$ .

Tap for more steps...

Step 5.1

Cancel the common factor.

$m = \frac{0 - (4)}{0 - (4)}$

Step 5.2

Rewrite the expression.

$m = 1$

Step 6

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

Tap for more steps...

Step 6.1

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

$y = m x + b$

Step 6.2

Substitute the value of $m$ into the equation.

$y = (1) \cdot x + b$

Step 6.3

Substitute the value of $x$ into the equation.

$y = (1) \cdot (4) + b$

Step 6.4

Substitute the value of $y$ into the equation.

$4 = (1) \cdot (4) + b$

Step 6.5

Find the value of $b$ .

Tap for more steps...

Step 6.5.1

Rewrite the equation as $(1) \cdot (4) + b = 4$ .

$(1) \cdot (4) + b = 4$

Step 6.5.2

Multiply $4$ by $1$ .

$4 + b = 4$

Step 6.5.3

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

Tap for more steps...

Step 6.5.3.1

Subtract $4$ from both sides of the equation.

$b = 4 - 4$

Step 6.5.3.2

Subtract $4$ from $4$ .

$b = 0$

Step 7

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.

$y = x$

Step 8