The line has a slope of -3, passes through the y-axis at the point (0, 18), and intersects the x-axis at the point (6, 0).
We can analyze the equation y + 9 = -3(x - 4) to determine the characteristics of the line:
Slope: To find the slope, we can rewrite the equation in slope-intercept form:
y = -3x + 18
From the slope-intercept form, the slope is represented by the coefficient of the x term, which is -3. Therefore, the line has a slope of -3.
Y-intercept: The y-intercept is the point where the line crosses the y-axis. In slope-intercept form, the y-intercept is represented by the constant term, which is 18. Therefore, the line passes through the y-axis at the point (0, 18).
Point of intersection with the x-axis: To find the point of intersection with the x-axis, we set y to zero and solve for x:
0 = -3x + 18
3x = 18
x = 6
Therefore, the line intersects the x-axis at the point (6, 0).
In summary, the line has a slope of -3, passes through the y-axis at the point (0, 18), and intersects the x-axis at the point (6, 0).