It looks like you've provided an equation of a line, which is \( y = -3x - 5 \). This is the equation in slope-intercept form (y = mx + b), where:
- The slope (m) is -3, which means that for every 1 unit increase in \( x \), \( y \) decreases by 3 units.
- The y-intercept (b) is -5, which means the line crosses the y-axis at \( (0, -5) \).
To analyze this line with respect to the x-axis and y-axis, we can:
1. Find the x-intercept:
To find the x-intercept, we set \( y = 0 \) and solve for \( x \):
\[ 0 = -3x - 5 \] \[ 3x = -5 \] \[ x = -\frac{5}{3} \approx -1.67 \]
So the x-intercept is approximately \( \left(-\frac{5}{3}, 0\right) \) or \( (-1.67, 0) \).
2. Summary of Intercepts:
- Y-intercept: \( (0, -5) \)
- X-intercept: \( \left(-\frac{5}{3}, 0\right) \) or approximately \( (-1.67, 0) \)
3. Sketching the Line:
To graph the line:
- Plot the y-intercept \( (0, -5) \).
- Plot the x-intercept \( (-1.67, 0) \).
- Draw a straight line through these points, extending in both directions.
Example Points
You can also calculate additional points to help sketch the line:
-
When \( x = 1 \): \[ y = -3(1) - 5 = -3 - 5 = -8 \quad (1, -8) \]
-
When \( x = -2 \): \[ y = -3(-2) - 5 = 6 - 5 = 1 \quad (-2, 1) \]
Plotting these additional points can provide more accuracy when drawing the line.
If you have any further specifics you'd like to explore regarding this equation or its graph, feel free to ask!