Precalculus Examples

$y - (- \frac{2}{5}) = \frac{1}{2} \cdot (x - \frac{1}{2})$

Step 1

Find the x-intercepts.

Tap for more steps...

Step 1.1

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$(0) - (- \frac{2}{5}) = \frac{1}{2} \cdot (x - \frac{1}{2})$

Step 1.2

Solve the equation.

Tap for more steps...

Step 1.2.1

Rewrite the equation as $\frac{1}{2} \cdot (x - \frac{1}{2}) = (0) - (- \frac{2}{5})$ .

$\frac{1}{2} \cdot (x - \frac{1}{2}) = (0) - (- \frac{2}{5})$

Step 1.2.2

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} \cdot (x - \frac{1}{2})) = 2 ((0) - (- \frac{2}{5}))$

Step 1.2.3

Simplify both sides of the equation.

Tap for more steps...

Step 1.2.3.1

Simplify the left side.

Tap for more steps...

Step 1.2.3.1.1

Simplify $2 (\frac{1}{2} \cdot (x - \frac{1}{2}))$ .

Tap for more steps...

Step 1.2.3.1.1.1

Apply the distributive property.

$2 (\frac{1}{2} x + \frac{1}{2} (- \frac{1}{2})) = 2 ((0) - (- \frac{2}{5}))$

Step 1.2.3.1.1.2

Combine $\frac{1}{2}$ and $x$ .

$2 (\frac{x}{2} + \frac{1}{2} (- \frac{1}{2})) = 2 ((0) - (- \frac{2}{5}))$

Step 1.2.3.1.1.3

Multiply $\frac{1}{2} (- \frac{1}{2})$ .

Tap for more steps...

Step 1.2.3.1.1.3.1

Multiply $\frac{1}{2}$ by $\frac{1}{2}$ .

$2 (\frac{x}{2} - \frac{1}{2 \cdot 2}) = 2 ((0) - (- \frac{2}{5}))$

Step 1.2.3.1.1.3.2

Multiply $2$ by $2$ .

$2 (\frac{x}{2} - \frac{1}{4}) = 2 ((0) - (- \frac{2}{5}))$

Step 1.2.3.1.1.4

Apply the distributive property.

$2 \frac{x}{2} + 2 (- \frac{1}{4}) = 2 ((0) - (- \frac{2}{5}))$

Step 1.2.3.1.1.5

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.2.3.1.1.5.1

Cancel the common factor.

$2 \frac{x}{2} + 2 (- \frac{1}{4}) = 2 ((0) - (- \frac{2}{5}))$

Step 1.2.3.1.1.5.2

Rewrite the expression.

$x + 2 (- \frac{1}{4}) = 2 ((0) - (- \frac{2}{5}))$

Step 1.2.3.1.1.6

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.2.3.1.1.6.1

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$x + 2 (\frac{- 1}{4}) = 2 ((0) - (- \frac{2}{5}))$

Step 1.2.3.1.1.6.2

Factor $2$ out of $4$ .

$x + 2 \frac{- 1}{2 (2)} = 2 ((0) - (- \frac{2}{5}))$

Step 1.2.3.1.1.6.3

Cancel the common factor.

$x + 2 \frac{- 1}{2 \cdot 2} = 2 ((0) - (- \frac{2}{5}))$

Step 1.2.3.1.1.6.4

Rewrite the expression.

$x + \frac{- 1}{2} = 2 ((0) - (- \frac{2}{5}))$

Step 1.2.3.1.1.7

Move the negative in front of the fraction.

$x - \frac{1}{2} = 2 ((0) - (- \frac{2}{5}))$

Step 1.2.3.2

Simplify the right side.

Tap for more steps...

Step 1.2.3.2.1

Simplify $2 ((0) - (- \frac{2}{5}))$ .

Tap for more steps...

Step 1.2.3.2.1.1

Multiply $- (- \frac{2}{5})$ .

Tap for more steps...

Step 1.2.3.2.1.1.1

Multiply $- 1$ by $- 1$ .

$x - \frac{1}{2} = 2 (0 + 1 (\frac{2}{5}))$

Step 1.2.3.2.1.1.2

Multiply $\frac{2}{5}$ by $1$ .

$x - \frac{1}{2} = 2 (0 + \frac{2}{5})$

Step 1.2.3.2.1.2

Add $0$ and $\frac{2}{5}$ .

$x - \frac{1}{2} = 2 (\frac{2}{5})$

Step 1.2.3.2.1.3

Multiply $2 (\frac{2}{5})$ .

Tap for more steps...

Step 1.2.3.2.1.3.1

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

$x - \frac{1}{2} = \frac{2 \cdot 2}{5}$

Step 1.2.3.2.1.3.2

Multiply $2$ by $2$ .

$x - \frac{1}{2} = \frac{4}{5}$

Step 1.2.4

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

Tap for more steps...

Step 1.2.4.1

Add $\frac{1}{2}$ to both sides of the equation.

$x = \frac{4}{5} + \frac{1}{2}$

Step 1.2.4.2

To write $\frac{4}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x = \frac{4}{5} \cdot \frac{2}{2} + \frac{1}{2}$

Step 1.2.4.3

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$x = \frac{4}{5} \cdot \frac{2}{2} + \frac{1}{2} \cdot \frac{5}{5}$

Step 1.2.4.4

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 1.2.4.4.1

Multiply $\frac{4}{5}$ by $\frac{2}{2}$ .

$x = \frac{4 \cdot 2}{5 \cdot 2} + \frac{1}{2} \cdot \frac{5}{5}$

Step 1.2.4.4.2

Multiply $5$ by $2$ .

$x = \frac{4 \cdot 2}{10} + \frac{1}{2} \cdot \frac{5}{5}$

Step 1.2.4.4.3

Multiply $\frac{1}{2}$ by $\frac{5}{5}$ .

$x = \frac{4 \cdot 2}{10} + \frac{5}{2 \cdot 5}$

Step 1.2.4.4.4

Multiply $2$ by $5$ .

$x = \frac{4 \cdot 2}{10} + \frac{5}{10}$

Step 1.2.4.5

Combine the numerators over the common denominator.

$x = \frac{4 \cdot 2 + 5}{10}$

Step 1.2.4.6

Simplify the numerator.

Tap for more steps...

Step 1.2.4.6.1

Multiply $4$ by $2$ .

$x = \frac{8 + 5}{10}$

Step 1.2.4.6.2

Add $8$ and $5$ .

$x = \frac{13}{10}$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(\frac{13}{10}, 0)$

Step 2

Find the y-intercepts.

Tap for more steps...

Step 2.1

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y - (- \frac{2}{5}) = \frac{1}{2} \cdot ((0) - \frac{1}{2})$

Step 2.2

Solve the equation.

Tap for more steps...

Step 2.2.1

Simplify $\frac{1}{2} \cdot ((0) - \frac{1}{2})$ .

Tap for more steps...

Step 2.2.1.1

Subtract $\frac{1}{2}$ from $0$ .

$y + \frac{2}{5} = \frac{1}{2} \cdot (- \frac{1}{2})$

Step 2.2.1.2

Multiply $\frac{1}{2} (- \frac{1}{2})$ .

Tap for more steps...

Step 2.2.1.2.1

Multiply $\frac{1}{2}$ by $\frac{1}{2}$ .

$y + \frac{2}{5} = - \frac{1}{2 \cdot 2}$

Step 2.2.1.2.2

Multiply $2$ by $2$ .

$y + \frac{2}{5} = - \frac{1}{4}$

Step 2.2.2

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

Tap for more steps...

Step 2.2.2.1

Subtract $\frac{2}{5}$ from both sides of the equation.

$y = - \frac{1}{4} - \frac{2}{5}$

Step 2.2.2.2

To write $- \frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$y = - \frac{1}{4} \cdot \frac{5}{5} - \frac{2}{5}$

Step 2.2.2.3

To write $- \frac{2}{5}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$y = - \frac{1}{4} \cdot \frac{5}{5} - \frac{2}{5} \cdot \frac{4}{4}$

Step 2.2.2.4

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 2.2.2.4.1

Multiply $\frac{1}{4}$ by $\frac{5}{5}$ .

$y = - \frac{5}{4 \cdot 5} - \frac{2}{5} \cdot \frac{4}{4}$

Step 2.2.2.4.2

Multiply $4$ by $5$ .

$y = - \frac{5}{20} - \frac{2}{5} \cdot \frac{4}{4}$

Step 2.2.2.4.3

Multiply $\frac{2}{5}$ by $\frac{4}{4}$ .

$y = - \frac{5}{20} - \frac{2 \cdot 4}{5 \cdot 4}$

Step 2.2.2.4.4

Multiply $5$ by $4$ .

$y = - \frac{5}{20} - \frac{2 \cdot 4}{20}$

Step 2.2.2.5

Combine the numerators over the common denominator.

$y = \frac{- 5 - 2 \cdot 4}{20}$

Step 2.2.2.6

Simplify the numerator.

Tap for more steps...

Step 2.2.2.6.1

Multiply $- 2$ by $4$ .

$y = \frac{- 5 - 8}{20}$

Step 2.2.2.6.2

Subtract $8$ from $- 5$ .

$y = \frac{- 13}{20}$

Step 2.2.2.7

Move the negative in front of the fraction.

$y = - \frac{13}{20}$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{13}{20})$

Step 3

List the intersections.

x-intercept(s): $(\frac{13}{10}, 0)$

y-intercept(s): $(0, - \frac{13}{20})$

Step 4