Algebra Examples

$(- 2, 0)$ and $(0, 5)$

Step 1

Find the slope of the line between $(- 2, 0)$ and $(0, 5)$ using $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ , which is the change of $y$ over the change of $x$ .

Tap for more steps...

Step 1.1

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 1.2

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 1.3

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

$m = \frac{5 - (0)}{0 - (- 2)}$

Step 1.4

Simplify.

Tap for more steps...

Step 1.4.1

Simplify the numerator.

Tap for more steps...

Step 1.4.1.1

Multiply $- 1$ by $0$ .

$m = \frac{5 + 0}{0 - (- 2)}$

Step 1.4.1.2

Add $5$ and $0$ .

$m = \frac{5}{0 - (- 2)}$

Step 1.4.2

Simplify the denominator.

Tap for more steps...

Step 1.4.2.1

Multiply $- 1$ by $- 2$ .

$m = \frac{5}{0 + 2}$

Step 1.4.2.2

Add $0$ and $2$ .

$m = \frac{5}{2}$

Step 2

Use the slope $\frac{5}{2}$ and a given point $(- 2, 0)$ to substitute for $x_{1}$ and $y_{1}$ in the point-slope form $y - y_{1} = m (x - x_{1})$ , which is derived from the slope equation $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (0) = \frac{5}{2} \cdot (x - (- 2))$

Step 3

Simplify the equation and keep it in point-slope form.

$y + 0 = \frac{5}{2} \cdot (x + 2)$

Step 4

Write the equation in standard form.

Tap for more steps...

Step 4.1

The standard form of a linear equation is $A x + B y = C$ .

Step 4.2

Multiply both sides by $2$ .

$2 (y + 0) = 2 (\frac{5}{2} \cdot (x + 2))$

Step 4.3

Simplify the left side.

Tap for more steps...

Step 4.3.1

Add $y$ and $0$ .

$2 y = 2 (\frac{5}{2} \cdot (x + 2))$

Step 4.4

Simplify the right side.

Tap for more steps...

Step 4.4.1

Simplify $2 (\frac{5}{2} \cdot (x + 2))$ .

Tap for more steps...

Step 4.4.1.1

Apply the distributive property.

$2 y = 2 (\frac{5}{2} x + \frac{5}{2} \cdot 2)$

Step 4.4.1.2

Combine $\frac{5}{2}$ and $x$ .

$2 y = 2 (\frac{5 x}{2} + \frac{5}{2} \cdot 2)$

Step 4.4.1.3

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.4.1.3.1

Cancel the common factor.

$2 y = 2 (\frac{5 x}{2} + \frac{5}{2} \cdot 2)$

Step 4.4.1.3.2

Rewrite the expression.

$2 y = 2 (\frac{5 x}{2} + 5)$

Step 4.4.1.4

Apply the distributive property.

$2 y = 2 \frac{5 x}{2} + 2 \cdot 5$

Step 4.4.1.5

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.4.1.5.1

Cancel the common factor.

$2 y = 2 \frac{5 x}{2} + 2 \cdot 5$

Step 4.4.1.5.2

Rewrite the expression.

$2 y = 5 x + 2 \cdot 5$

Step 4.4.1.6

Multiply $2$ by $5$ .

$2 y = 5 x + 10$

Step 4.5

Rewrite the equation.

$5 x + 10 = 2 y$

Step 4.6

Move all terms containing variables to the left side of the equation.

Tap for more steps...

Step 4.6.1

Subtract $2 y$ from both sides of the equation.

$5 x + 10 - 2 y = 0$

Step 4.6.2

Move $10$ .

$5 x - 2 y + 10 = 0$

Step 4.7

Subtract $10$ from both sides of the equation.

$5 x - 2 y = - 10$

Step 5