Writing Equations from Graphs Made Easy
A Step-by-Step Guide for 8th Grade Math Master Slope-Intercept, Point-Slope, and Standard Forms
What We'll Learn Today
How to identify points on a coordinate plane Understanding slope using rise over run Three ways to write linear equations When to use each equation form Step-by-step problem solving strategies
The Coordinate Plane Basics
X-axis runs horizontally (left to right) Y-axis runs vertically (up and down) Origin is where axes meet (0,0) Points are written as (x, y) First number is x-coordinate, second is y-coordinate
Practice: Finding Points
Look at the graph on your worksheet Identify the coordinates of points A, B, and C Remember: (x, y) format Check your answers with a partner
Understanding Slope: Rise Over Run
Slope measures how steep a line is Rise = vertical change (up or down) Run = horizontal change (left or right) Slope = Rise ÷ Run Positive slope goes up, negative slope goes down
Slope Examples
{"left":"From (1,2) to (3,6): Rise = 4, Run = 2, Slope = 4/2 = 2\nFrom (0,5) to (2,1): Rise = -4, Run = 2, Slope = -4/2 = -2","right":"From (1,3) to (4,3): Rise = 0, Run = 3, Slope = 0/3 = 0\nFrom (2,1) to (2,5): Rise = 4, Run = 0, Slope = undefined"}
Slope-Intercept Form: y = mx + b
m = slope of the line b = y-intercept (where line crosses y-axis) Most common form for graphing Easy to identify slope and y-intercept Example: y = 2x + 3 means slope = 2, y-intercept = 3
Your Turn: Slope-Intercept Practice
Look at Graph #1 on your worksheet Find the y-intercept (where does it cross the y-axis?) Pick two points and calculate the slope Write the equation in y = mx + b form
Point-Slope Form: y - y₁ = m(x - x₁)
Use when you know slope and one point x₁ and y₁ are coordinates of the known point m is the slope Useful when y-intercept isn't obvious Can convert to slope-intercept form by solving for y
Standard Form: Ax + By = C
A, B, and C are integers (whole numbers) A should be positive No fractions or decimals Useful for certain types of problems Can find x and y intercepts easily
When to Use Each Form
{"left":"Slope-Intercept (y = mx + b): When graphing lines or when slope and y-intercept are obvious\nPoint-Slope (y - y₁ = m(x - x₁)): When you know slope and any point on the line","right":"Standard Form (Ax + By = C): When finding intercepts or working with integer coefficients\nAll forms represent the same line, just written differently"}
Quick Check: Which Form Would You Use?
Scenario 1: You can see the line crosses the y-axis at 4 and has a slope of 2 Scenario 2: The line passes through (3, 5) and has a slope of -1 Scenario 3: You need to find where the line crosses both axes Discuss with your partner and be ready to explain your reasoning
33 more slides available after you open the deck.
Download all 45 slidesMore Math slide decks
Other ready-to-teach math decks for US classrooms.
Adding with Partial Sums Grade 3
Multiplication: Equal Groups and Arrays
Multiplication: Equal Groups and Arrays
Theoretical Probability: Predicting Mathematical Outcomes
Theoretical Probability: Predicting Mathematical Outcomes
