Algebra Examples

$2 x - 4 y = 3$

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 $x$ .

$2 x - 4 \cdot 0 = 3$

Step 1.2

Solve the equation.

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Step 1.2.1

Simplify $2 x - 4 \cdot 0$ .

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Step 1.2.1.1

Multiply $- 4$ by $0$ .

$2 x + 0 = 3$

Step 1.2.1.2

Add $2 x$ and $0$ .

$2 x = 3$

Step 1.2.2

Divide each term in $2 x = 3$ by $2$ and simplify.

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Step 1.2.2.1

Divide each term in $2 x = 3$ by $2$ .

$\frac{2 x}{2} = \frac{3}{2}$

Step 1.2.2.2

Simplify the left side.

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Step 1.2.2.2.1

Cancel the common factor of $2$ .

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Step 1.2.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{3}{2}$

Step 1.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{3}{2}$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(\frac{3}{2}, 0)$

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 $y$ .

$2 (0) - 4 y = 3$

Step 2.2

Solve the equation.

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Step 2.2.1

Simplify $2 (0) - 4 y$ .

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Step 2.2.1.1

Multiply $2$ by $0$ .

$0 - 4 y = 3$

Step 2.2.1.2

Subtract $4 y$ from $0$ .

$- 4 y = 3$

Step 2.2.2

Divide each term in $- 4 y = 3$ by $- 4$ and simplify.

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Step 2.2.2.1

Divide each term in $- 4 y = 3$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{3}{- 4}$

Step 2.2.2.2

Simplify the left side.

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Step 2.2.2.2.1

Cancel the common factor of $- 4$ .

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Step 2.2.2.2.1.1

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{3}{- 4}$

Step 2.2.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{3}{- 4}$

Step 2.2.2.3

Simplify the right side.

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Step 2.2.2.3.1

Move the negative in front of the fraction.

$y = - \frac{3}{4}$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{3}{4})$

Step 3

List the intersections.

x-intercept(s): $(\frac{3}{2}, 0)$

y-intercept(s): $(0, - \frac{3}{4})$

Step 4