Picture a line tilted down like a seesaw. Shade the area below. That's where x - 3y < 3 lives! The line itself crosses the x-axis at 3 (that's the x-intercept) and cuts the y-axis at -1 (that's the y-intercept). Now you can graph it in a flash!
Here's how to find the graph and intercepts of the inequality x - 3y < 3:
1. Graphing the Inequality:
- Rewrite the inequality as an equality:** x - 3y = 3. This gives you the equation of the boundary line.
- Plot the boundary line:** A dashed line as it represents an inequality (<).
- Divide the plane into two regions:** Above the line (y > 1/3x - 1) satisfies x - 3y > 3 and is shaded, while below the line (y < 1/3x - 1) satisfies x - 3y < 3 and remains unshaded.
2. X-intercept:
- The x-intercept is the point where the line crosses the x-axis, which happens when y is 0.
- Set y = 0 in the equation: x - 3(0) = 3 --> x = 3.
- Therefore, the x-intercept is (3, 0).
3. Y-intercept:
- The y-intercept is the point where the line crosses the y-axis, which happens when x is 0.
- Set x = 0 in the equation: 0 - 3y = 3 --> y = -1.
- Therefore, the y-intercept is (0, -1).
- The graph of x - 3y < 3 is a shaded region below the dashed line y = 1/3x - 1.
- The x-intercept is (3, 0).
- The y-intercept is (0, -1).
I hope this explanation helps! Let me know if you have any other questions.