Warm Up
Use the Desmos graphing tool or technology outside the course. Graph the following lines given in slope-intercept form.
Compare your answers:
What is the relationship between the two lines you graphed in question 1?
Compare your answer:
They are parallel lines.
When you examine the equations of the lines, what do you notice is the same about the equations?
Compare your answer: Your answer may vary, but here are some samples.
- The slopes of the lines are equal.
- The numbers in front of the variables are the same.
When you examine the equations of the lines, what do you notice is different about the equations?
Compare your answer: Your answer may vary, but here are some samples.
- The constant term is different in each equation.
- The number that is added to the equation is different.
- The -intercepts for each equation is different.
When you examine the graph of the lines, how many vertical spaces are between the two lines?
There are 6 vertical spaces between the two lines.
Use the graphing tool above or technology outside the course, on your coordinate grid, use the slope and -intercept of each equation to graph each equation. Use a different color for each equation.
Compare your answers:
When you examine the graph of the lines in question 6, explain if the lines appear to be perpendicular.
Compare your answer: Your answer may vary, but here is a sample.
- No, the lines don't look like they intersect at right angles - so they don't look like they are perpendicular. (Check the settings of your graph, this is incorrect.)
- Yes, the lines look like they intersect at right angles - so they appear perpendicular. (This is the correct answer.)
Sometimes lines that are perpendicular do not appear to intersect at right angles because of the settings of the graph. To more easily identify perpendicular lines, change the settings of your Desmos graph. In your graph, select the “wrench tool” icon. In the grid section of the menu that pops up, select the “Zoom Square” option.
Remember to identify perpendicular lines algebraically, examine their slopes. If the slope values are opposite reciprocals, then the lines intersect at right angles and are perpendicular.