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
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