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Slope and Similar Triangles




 
Videos, lessons, and solutions to help Grade 8 students learn how to use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b

Common Core: 8.EE.6

Suggested Learning Targets

  • I can find the slope of a line between a pair of distinct points.
  • I can determine the y-intercept of a line.
  • I can interpret unit rate as the slope of the graph.
  • I can analyze patterns for points on a line through the origin
  • I can derive an equation of the form y =m x for a line through the origin
  • I can analyze patterns for points on a line that does not pass through or include the origin
  • I can derive an equation of the form y = mx + b for a line intercepting the vertical axis at b (the y-intercept)
  • I can use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane

Related Topics:
Common Core for Grade 8
Common Core for Mathematics
More Math Lessons for Grade 8

Use similar triangles to explain equal slopes (8.EE.6)

How to find the Slope of a Line Using Similar Right Triangles?
The slope of a line can be created by drawing a right triangle from one point of the line to another point on the line. Similar triangles to prove that the slope is constant for a line
Example that involves slope and triangle similarity
Use the graph below to decide which of the following equations are true.



How to find the slope a line given the graph?
The slope is obtained by the vertical change (rise) divided by the horizontal change (run).
A line has a positive slope if it is going uphill from left to right.
A line has a negative slope if it is going downhill from left to right.

How to use the slope equation to find slope given two points?
Examples:
1. Find the slope of the line that passes through the points (-2, -2) and (4, 1)
2. Find the slope of the line that passes through the points (3, 5) and (-1, 4)
3. Find the slope of the line that passes through the points (-5, 3) and (2, 1)

What is the slope of a horizontal line?
The slope of a horizontal line is 0.

What is the slope of a vertical line?
The slope of a vertical line is undefined

How to graph a line given an ordered pair and slope?
Example:
1. Draw a line through the point (2, 0) that has a slope of 3.
How to find the slope of a line given an equation in the form y = mx + b?
1. The slope is the number in front of x when the equation is in the form y = mx + b
2. m = slope
3. slope = rise/run How to graph a line from an equation?
Examples:
1. Graph the line y = 1/2x - 2
2. Graph y = -3x + 7
3. Graph y = 5/3x -10


 
Interpret The Rate of Change/Slope and Intercepts Within the Context of Everyday
Examples:
1. Jessica's assignment was to go out and find a staircase, then find the slope of the staircase. Given a picture of Jessica's staircase, find its slope.

2. Zachary loves running the 400 meter race. He decides to calculate his rate while running the race. He collects data for 5 races. Find his average rate (slope) over the 5 races.

3. Cee-cee's parents have decided that she can get a cell phone as long as she pays the monthly bill. Given a copy of her first bill find the slope and y-intercept of the information?

4. Connor is saving his money to buy a Playstation 3 and all the accessories that he desires. Currently, he has $127.00 saved. He plans on saving $7 of his weekly allowance. Write an equation in slope-intercept form that would describe Connor's financial plan. From this equation determine how much money Connor will have after 8 weeks.

5. The graph below shows Jenny's walk from home to the grocery store to get ice cream sandwiches.
a) How far away is Jenny's house from the grocery store?
b) Determine how fast (slope) she walked on the way home.
c) What do the horizontal lines mean in Jenny's story? 8.EE.6, Slope Intercept Form 8.EE.6, Zero and Undefined Slopes

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