In Exercises 67–72, use intercepts to graph each equation. 6x-9y-18 = 0

Verified step by step guidance

1. To find the x-intercept, set \( y = 0 \) in the equation \( 6x - 9y - 18 = 0 \) and solve for \( x \).
2. To find the y-intercept, set \( x = 0 \) in the equation \( 6x - 9y - 18 = 0 \) and solve for \( y \).
3. Plot the x-intercept and y-intercept on the coordinate plane.
4. Draw a straight line through the two intercepts to graph the equation.
5. Verify the line by checking if another point on the line satisfies the original equation.

Key Concepts

Intercepts

Intercepts are points where a graph intersects the axes. The x-intercept occurs where the graph crosses the x-axis (y=0), and the y-intercept occurs where it crosses the y-axis (x=0). Finding these points is essential for graphing linear equations, as they provide key coordinates that define the line's position.

Linear Equations

A linear equation is an equation of the first degree, meaning it can be expressed in the form Ax + By + C = 0, where A, B, and C are constants. The graph of a linear equation is a straight line, and understanding its structure helps in identifying its slope and intercepts, which are crucial for graphing.

Graphing Techniques

Graphing techniques involve methods used to visually represent equations on a coordinate plane. For linear equations, the most common technique is to plot the intercepts and then draw a straight line through these points. This approach simplifies the graphing process and ensures accuracy in representing the equation.