Finding Slope on a Graph
Grade 8 Mathematics Understanding Linear Relationships Rise Over Run
What is Slope?
Slope measures steepness of a line Shows rate of change Tells us how y changes as x increases Can be positive, negative, zero, or undefined
Rise Over Run Method
Rise = vertical change (up or down) Run = horizontal change (left or right) Slope = Rise ÷ Run Always move from left to right
Practice: Find the Slope
Look at the line on the coordinate plane Count the rise (vertical change) Count the run (horizontal change) Calculate: slope = rise ÷ run
The Slope Formula
m = (y₂ - y₁) ÷ (x₂ - x₁) m represents slope Use any two points on the line Subtract coordinates: second minus first
Linear Equations: y = mx + b
m = slope of the line b = y-intercept (where line crosses y-axis) x and y are coordinates of any point This form shows slope directly
Writing Equations from Graphs
{"left":"Step 1: Find the y-intercept (b)\nStep 2: Choose two clear points\nStep 3: Calculate slope (m)\nStep 4: Write equation y = mx + b","right":"Example: Line through (0,3) and (2,7)\ny-intercept = 3, so b = 3\nSlope = (7-3)÷(2-0) = 4÷2 = 2\nEquation: y = 2x + 3"}
Real-World Application
A hiking trail rises 300 feet over a horizontal distance of 1,200 feet. What is the slope of this trail? How would you write this as a percentage?