In the applet below is to help review the concepts of slope. You will be asked to manipulate the equation y=mx+b to help find equations of different types of lines.
Make sure all boxes are un-checked to start. Start by clicking on the checkbox that says f(x)=M(x)+b. Begin by moving the colorful sliders above. What does M do to the equation? What does B do to the equation? What do both do to the equation as a whole? What do we call both M and B?
Uncheck this box and check the box that says y=2x+3. What is similar about these lines? Click and drag C. Does the line have the same slope everywhere you Drag it? Will the lines ever intersect? Click on the first slope box. Are the slopes the same? Drag C around to make sure. From equation d we can see that the slope will always be the same. What is happening to the B term as we move C around?
Now uncheck Line 1 and Slope and check Line 2. What is different about this equation? Does this equation intersect our line y=2x+3? What angle does it look like the two lines intersect at? Drag point A around and see if your conjectures hold. Click on Slope. What kind of lines are these? What is the difference between these two slopes? What do we call these two numbers?
Now check boxes Parallel through point D and Perpendicular to point E. From previous lesson, use what we know to create a parallel line through point D and a perpendicular line through point E. We are given a slope of the parent line and a point. So, how do we go about doing this? Show all work.