Find the Domain and Range x-4y=10

$x - 4 y = 10$

Step 1

Subtract $x$ from both sides of the equation.

$- 4 y = 10 - x$

Step 2

Divide each term in $- 4 y = 10 - x$ by $- 4$ and simplify.

Divide each term in $- 4 y = 10 - x$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{10}{- 4} + \frac{- x}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{10}{- 4} + \frac{- x}{- 4}$

Divide $y$ by $1$ .

$y = \frac{10}{- 4} + \frac{- x}{- 4}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $10$ and $- 4$ .

Factor $2$ out of $10$ .

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

Cancel the common factors.

Factor $2$ out of $- 4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Dividing two negative values results in a positive value.

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

Step 3

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 4

The range is the set of all valid $y$ values. Use the graph to find the range.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${y | y \in ℝ}$

Step 5

Determine the domain and range.

Domain: $(- \infty, \infty), {x | x \in ℝ}$

Range: $(- \infty, \infty), {y | y \in ℝ}$

Step 6

Find the Domain and Range x-4y=10

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