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Begin by graphing the equations. First two equations represent horizontal lines and last two of them are in slope-intercept form.
(3/2,3), (7/2,7), (8,3), (10,7)
Let's examine the given equations. y=3 y=7 y=2x y=2x-13 Equation I and Equation II represent horizontal lines that pass through the points (0,3) and (0,7), respectively. Let's graph the first two equations.
Now we have two points, we can draw a line.
The last equation is also in slope-intercept form, so it can be graphed proceeding in the same way. Equation IV y= 2x -13 Let's graph it!
The y-coordinates of the vertices are already known. We will find the x-coordinates of them by substituting y=3 and y=7 into Equation III and Equation IV. Let's begin by substituting y=3 into Equation III.
The coordinates of the first vertex is ( 32,3). The other vertices can be found in the same way.
| Vertex | y-coordinate | Substitution | x-coordinate | Point |
|---|---|---|---|---|
| I | 3 | 3=2x | 3/2 | (3/2,3) |
| II | 7 | 7=2x | 7/2 | (7/2,7) |
| III | 3 | 3=2x-13 | 8 | (8,3) |
| IV | 7 | 7=2x-13 | 10 | (10,7) |