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 one solution. To do this, we can write two lines that have different slopes and different y-intercepts.
y= 4x+ 1 & (I) y= -1x+ 6 & (II) ⇒ y=4x+1 & (I) y=- x+6 & (II)
Now we will use a graph to make sure that our example system is correct. Let's plot points (0, 1) and (0, 6) that represent the y-intercepts of both equations.
Next we will use slopes to draw another point for each line. In both cases we will start at the y-intercepts. For Equation 1 we will move 1 unit right and 4 units up. For Equation 2 we will move 1 unit right and 1 unit down.
Finally we will connect the points with smooth lines.
We can see that the lines have one point of intersection. This confirms that there is one solution to our example system.
