Calculus Examples

$y = \frac{9}{4} x - \frac{1}{4}$

Step 1

Find the x-intercepts.

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Step 1.1

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

$0 = \frac{9}{4} x - \frac{1}{4}$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $\frac{9}{4} x - \frac{1}{4} = 0$ .

$\frac{9}{4} x - \frac{1}{4} = 0$

Step 1.2.2

Combine $\frac{9}{4}$ and $x$ .

$\frac{9 x}{4} - \frac{1}{4} = 0$

Step 1.2.3

Add $\frac{1}{4}$ to both sides of the equation.

$\frac{9 x}{4} = \frac{1}{4}$

Step 1.2.4

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$9 x = 1$

Step 1.2.5

Divide each term in $9 x = 1$ by $9$ and simplify.

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Step 1.2.5.1

Divide each term in $9 x = 1$ by $9$ .

$\frac{9 x}{9} = \frac{1}{9}$

Step 1.2.5.2

Simplify the left side.

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Step 1.2.5.2.1

Cancel the common factor of $9$ .

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Step 1.2.5.2.1.1

Cancel the common factor.

$\frac{9 x}{9} = \frac{1}{9}$

Step 1.2.5.2.1.2

Divide $x$ by $1$ .

$x = \frac{1}{9}$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(\frac{1}{9}, 0)$

Step 2

Find the y-intercepts.

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Step 2.1

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

$y = \frac{9}{4} \cdot (0) - \frac{1}{4}$

Step 2.2

Solve the equation.

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Step 2.2.1

Multiply $\frac{9}{4}$ by $0$ .

$y = \frac{9}{4} \cdot 0 - \frac{1}{4}$

Step 2.2.2

Remove parentheses.

$y = \frac{9}{4} \cdot (0) - \frac{1}{4}$

Step 2.2.3

Simplify $\frac{9}{4} \cdot (0) - \frac{1}{4}$ .

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Step 2.2.3.1

Multiply $\frac{9}{4}$ by $0$ .

$y = 0 - \frac{1}{4}$

Step 2.2.3.2

Subtract $\frac{1}{4}$ from $0$ .

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

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{1}{4})$

Step 3

List the intersections.

x-intercept(s): $(\frac{1}{9}, 0)$

y-intercept(s): $(0, - \frac{1}{4})$

Step 4