Mathematics
Grade 8
15 min
Write an equation from a graph using a table
Write an equation from a graph using a table
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1
Introduction & Learning Objectives
Learning Objectives
Identify ordered pairs accurately from a given graph.
Organize identified ordered pairs into a table of values.
Calculate the slope (rate of change) from a table of values.
Determine the y-intercept from a graph or table.
Formulate a linear equation in slope-intercept form (y = mx + b) from a graph using a table.
Verify the derived equation using other points from the graph.
Ever wondered how scientists predict future trends from data points on a chart? 📈 It all starts with understanding the mathematical relationship between those points!
In this lesson, you'll learn a powerful method to turn a visual graph into a mathematical equation. We'll use tables to organize information from graphs, helping us uncover the hidden rule that connects the x...
2
Key Concepts & Vocabulary
TermDefinitionExample
GraphA visual representation of the relationship between two variables, typically x and y, plotted on a coordinate plane.A line drawn on a grid showing how a person's height changes with age.
Ordered Pair (Coordinate)A pair of numbers (x, y) that represents a single point's location on a graph, where 'x' is the horizontal position and 'y' is the vertical position.The point (3, 5) means 3 units right on the x-axis and 5 units up on the y-axis.
Table of ValuesAn organized list that shows the relationship between two variables, typically x and y, by listing corresponding ordered pairs in columns or rows.A table showing (x: 0, y: 2), (x: 1, y: 4), (x: 2, y: 6).
Slope (Rate of Change)A measure of the steepness of a line, indicating how much t...
3
Core Formulas
Slope Formula
m = \frac{y_2 - y_1}{x_2 - x_1}
This formula is used to calculate the slope (m) of a line given any two distinct points (x_1, y_1) and (x_2, y_2) from the table or graph. Ensure you subtract the y-values in the same order as the x-values.
Slope-Intercept Form of a Linear Equation
y = mx + b
This is the standard form for writing a linear equation, where 'm' represents the slope and 'b' represents the y-intercept. Our goal is to find 'm' and 'b' to write the equation.
Identifying the Y-intercept
The y-intercept 'b' is the y-value when x = 0.
To find 'b', look for the point (0, y) on the graph or in your table of values. The y-value of this point is your y-intercept. If (0,y) is not directly visib...
5 more steps in this tutorial
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Sign Up Free to ContinueSample Practice Questions
Challenging
A table of values for a line contains the points (-5, 15) and (4, -3). What is the equation of the line?
A.y = -2x + 5
B.y = 2x + 25
C.y = -5x - 10
D.y = 5x + 40
Challenging
A graph shows a horizontal line passing through the points (-3, 4), (0, 4), and (2, 4). Which equation represents this line?
A.x = 4
B.y = 4
C.y = x + 4
D.y = 0x + 0
Challenging
A student is given a graph of a line passing through (0, 4) and (2, 10). They correctly identify the y-intercept as b=4. They then write the equation y = 2x + 4. What was their conceptual error?
A.They used the y-coordinate of the second point as the slope.
B.They calculated the slope incorrectly.
C.They used the x-coordinate of the second point as the slope.
D.They confused the slope and y-intercept in the final equation.
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