Final answer:
To find the area of the triangle formed by the x-axis, the y-axis, and the line -2x=9y-18, we need to find the x-intercept and y-intercept of the line. Then, we can create a right triangle with the x and y-intercepts and use the formula for finding the area of a triangle. The area of the triangle is 2 square units.
Step-by-step explanation:
To find the area of the triangle formed by the x-axis, the y-axis, and the line -2x=9y-18, we need to find the points where the line intersects the x-axis and the y-axis. To find the x-intercept (where the line intersects the x-axis), we set y=0 and solve for x. Similarly, to find the y-intercept (where the line intersects the y-axis), we set x=0 and solve for y. Once we have the x and y intercepts, we can create a right triangle by connecting these points to the origin (0,0). Finally, we use the formula for finding the area of a triangle, which is A = (base * height) / 2, where the base is the length of the x-axis and the height is the length of the y-axis.
Let's solve for the x-intercept:
-2x = 9y - 18
0 = 9y - 18
9y = 18
y = 2
The x-intercept is (2, 0).
Now let's solve for the y-intercept:
-2x = 9y - 18
-2(0) = 9y - 18
0 = 9y -18
y = 2
The y-intercept is (0, 2).
The base of the triangle is the x-coordinate of the x-intercept, which is 2. The height of the triangle is the y-coordinate of the y-intercept, which is 2. Substituting these values into the formula, we get:
A = (2 * 2) / 2 = 2
Therefore, the area of the triangle formed by the x-axis, the y-axis, and the line -2x=9y-18 is 2 square units.