Question

graph the line \\(-5y - 3x = 0\\). give the domain and range.

part 1 of 3
use the graphing tool to graph the equation.

Explanation:

⚡ Using what you learned: graphing linear equations · domain and range

Step 1: Rewrite in slope-intercept form

Solve the equation for \( y \) to find the slope and the \( y \)-intercept:

$$ -5y - 3x = 0 $$

$$ -5y = 3x $$

$$ y = -\frac{3}{5}x $$

The \( y \)-intercept is \( (0, 0) \) and the slope is \( -\frac{3}{5} \).

Step 2: Find two points on the line

Use the equation \( y = -\frac{3}{5}x \) to find two points to plot:

• If \( x = 0 \):

$$ y = -\frac{3}{5}(0) = 0 \implies (0, 0) $$

• If \( x = -5 \):

$$ y = -\frac{3}{5}(-5) = 3 \implies (-5, 3) $$

• If \( x = 5 \):

$$ y = -\frac{3}{5}(5) = -3 \implies (5, -3) $$

Plot the line using any two of these points, such as \( (0, 0) \) and \( (5, -3) \).

Step 3: Determine domain and range

Since this is a non-vertical, non-horizontal straight line that extends infinitely in both directions:

• Domain: \( (-\infty, \infty) \)
• Range: \( (-\infty, \infty) \)

Answer:

• Graph: A straight line passing through the points \( (0, 0) \) and \( (5, -3) \).
• Domain: \( (-\infty, \infty) \)
• Range: \( (-\infty, \infty) \)