Lines have the same slopes but different y-intercepts
Lines have the same slopes and y-intercepts
In our exercise, we want to write a system of linear equations that has infinitely many solutions. To do this, we can write two lines that have the same slope and the same y-intercepts.
y= -2x+ 3 & (I) y= -2x+ 3 & (II)
However, before we graph the lines we can rewrite the second equation using the Properties of Equality. This will make our equations look different with no change in the solution.
Now we will use a graph to make sure that our example system is correct. Let's plot point (0, 3) that represents the y-intercept of both equations. Since the equations have the same slope and y-intercept, they are represented by the same line.
Next we will use the slope to draw another point for our line. Since both equations have a slope of -2, we will start at the y-intercepts and then move 1 unit right and 2 units down.
Finally we will connect the points with a smooth line. Remember that this line represents both equations.
Notice that this is only an example solution, because we can think of infinitely many example systems that satisfy the conditions.
