8th Grade Slope and Similar Triangles Lesson (Free PDF)
This slope similar triangles lesson for 8th Grade covers slope and similar triangles (Common Core 8.EE.B.6), with a free PDF to print.
The slope of a line is the same between any two points because the right triangles formed by rise and run are similar. A line with slope m through the origin has equation y = mx, and a line with slope m and y-intercept b has equation y = mx + b. Slope equals rise divided by run.
Grade 8 · Common Core State Standards: 8.EE.B.6
Key facts in this slope similar triangles lesson
- Slope \(m = \frac{\text{rise}}{\text{run}} = \frac{y_{2} – y_{1}}{x_{2} – x_{1}}\).
- Any two points on a line give the same slope because the triangles are similar.
- \(y = mx\) goes through the origin; \(y = mx + b\) crosses the y-axis at \((0, b)\).
- Parallel lines have equal slopes; horizontal lines have slope 0.
- To write an equation, find \(m\), then solve for \(b\) with a point.
Why is the slope the same between any two points on a line?
Pick two points on a line and draw a right triangle with a horizontal leg (the run) and a vertical leg (the rise). Any two such triangles on the same line have the same angles, so they are similar. Similar triangles have proportional sides, so \(\frac{\text{rise}}{\text{run}}\) is the same for both.
Small triangle: \(\frac{3}{2}\). Large triangle: \(\frac{6}{4} = \frac{3}{2}\). The slope is constant, so we can call it \(m\).
How do you read slope and intercept from an equation?
In \(y = 2x + 1\), the slope is \(m = 2\) and the y-intercept is \(b = 1\). Start at \((0, 1)\), go up 2 and right 1 to reach \((1, 3)\), then repeat.
How do you write the equation of a line?
- Find the slope from two points: \(m = \frac{y_{2} – y_{1}}{x_{2} – x_{1}}\).
- Substitute one point and \(m\) into \(y = mx + b\) to find \(b\).
- Write the equation.
- Check with the other point.
Worked example. A line passes through \((1, 4)\) and \((3, 10)\). The slope is \(\frac{10 – 4}{3 – 1} = 3\). Substitute \((1, 4)\): \(4 = 3 \cdot 1 + b\), so \(b = 1\). The equation is \(y = 3x + 1\). Check: \(3 \cdot 3 + 1 = 10\).
Lines with the same slope are parallel. A horizontal line has slope 0, so its equation is \(y = b\). Negative slopes go down from left to right.
Slope similar triangles lesson: questions and answers
What are rise and run?
Rise is the vertical change between two points, and run is the horizontal change. Slope is rise divided by run.
Does it matter which point I call the first point?
No, as long as you subtract in the same order for y and x. \(\frac{10 – 4}{3 – 1}\) and \(\frac{4 – 10}{1 – 3}\) both equal 3.
What is the slope of a horizontal line?
Zero, because the rise is 0. A horizontal line through \((0, 5)\) is \(y = 5\). A vertical line has undefined slope.
How can I find b if I know the slope and a point?
Substitute the point into \(y = mx + b\) and solve. For slope 2 and point \((3, 11)\): \(11 = 6 + b\), so \(b = 5\).
How do I rewrite 2x + y = 6 as y = mx + b?
Subtract \(2x\) from both sides: \(y = -2x + 6\). Now the slope is -2 and the y-intercept is 6.
How to use this slope similar triangles lesson
Read the definitions first, then follow the worked method line by line and redo the example on paper without looking. When every step makes sense, move on to the worksheet, then check yourself with the quiz.
Download the slope similar triangles lesson as a PDF with the button below and keep it with your notes.
All Grade 8 chapters: Grade 8 math.
More 8th Grade math
Lessons
See all
Worksheets
See all
Tests
See all
Scatter Plots and Association Test with Point Values- Slope and Similar Triangles Test with Point Values
- Scientific Notation Test with Point Values
- Angles in Triangles and Parallel Lines Test with Point Values
- Dilations and Similar Figures Test with Point Values
- Systems of Linear Equations Test with Point Values
