Answer:
- see attached for a graph
- centroid: (0, 2)
Explanation:
You want the graphs of the given lines, and the centroid of the triangle they form.
- y1 = 3x -4
- y2 = 3/4x +5
- y3 = -3/2x -4
Graph
It works well to start by plotting the y-intercept of each equation, then using the slope to identify the "rise" and "run" to another point on the line. Then the line can be drawn through the points.
- y1: y-intercept = (0, -4); additional point 3 up and 1 over: (1, -1).
- y2: y-intercept = (0, 5); additional point 3 up and 4 over: (4, 8).
- y3: y-intercept = (0, -4); additional point 3 down and 2 over: (2, -7). This one is more easily plotted in the reverse direction, 3 up and 2 to the left: (-2, -1).
Vertices
The graph shows you the points of intersection of the lines are ...
(-4, 2), (4, 8), (0, -4) . . . . . . . . . the last is the y-intercepts of y1 and y3
Centroid
The centroid coordinates are the average of the vertex coordinates, their sum divided by 3.
centroid = ((-4, 2) +(4, 8) +(0, -4))/3 = (-4+4+0, 2+8-4)/3 = (0, 6)/3
centroid = (0, 2)
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Additional comment
The slope of each line is the x-coefficient in the equation. That slope is the ratio of "rise" (change in y) to "run" (change in x) for the line. It is often convenient to draw a graph by finding points on the line counting the grid squares for rise and run.