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
Extract coordinate pairs from a given linear graph.
Organize coordinate pairs into a table of values.
Calculate the slope (rate of change) of a line using points from a table.
Identify the y-intercept of a line from a graph or table.
Write the equation of a line in slope-intercept form ($y = mx + b$) from a graph using a table.
Verify the derived equation by checking additional points from the graph.
Ever wondered how scientists predict future trends from data plots? 📈 It all starts with understanding the relationship shown in a graph!
In this lesson, you'll learn a powerful method to translate visual information from a graph into a mathematical equation. By using a table to organize data points, you'll uncover the hidden rule that defines the...
2
Key Concepts & Vocabulary
TermDefinitionExample
Linear EquationAn equation whose graph is a straight line. It describes a constant rate of change between two variables.$y = 2x + 3$ is a linear equation, where 'x' and 'y' are variables.
GraphA visual representation of the relationship between two or more variables, often plotted on a coordinate plane.A line drawn on an x-y plane showing how a plant's height changes over days.
Table of ValuesAn organized list that shows the corresponding values of two variables, typically 'x' and 'y', for points on a graph.A table with columns for 'x' and 'y', listing points like (0, 3), (1, 5), (2, 7).
Slope (Rate of Change)A measure of the steepness and direction of a line, calculated as the ratio of the vertical cha...
3
Core Formulas
Slope Formula
$m = \frac{y_2 - y_1}{x_2 - x_1}$
Use this formula to calculate the slope ('m') of a line given any two distinct points $(x_1, y_1)$ and $(x_2, y_2)$ from the graph or table. The order of subtraction must be consistent for both x and y.
Slope-Intercept Form of a Linear Equation
$y = mx + b$
This is the standard form for writing the equation of a straight line. 'm' represents the slope, and 'b' represents the y-coordinate of the y-intercept (where the line crosses the y-axis, at point $(0, b)$).
Finding the Y-intercept ('b')
If $(0, y)$ is a point on the line, then $b = y$. If not, substitute a known point $(x, y)$ and the calculated slope 'm' into $y = mx + b$ and solve for 'b'.
The y-intercept...
4 more steps in this tutorial
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Challenging
A student is finding the equation for a line passing through (-1, 8) and (1, 2). Their work is:
Step 1: m = (2 - 8) / (1 - (-1)) = -6 / 2 = -3.
Step 2: Use (1, 2) -> 2 = -3(1) + b -> 2 = -3 + b.
Step 3: b = 2 - 3 = -1.
Step 4: Equation is y = -3x - 1.
In which step did the student make a mistake?
A.Step 1: The slope calculation is incorrect.
B.Step 2: They substituted the wrong point.
C.Step 4: The final equation is in the wrong form.
D.Step 3: The algebraic step to solve for 'b' is incorrect.
Challenging
A graph of a line is provided. A partial table of values is shown below. What is the value of 'k' and the equation of the line?
x | y
---|---
-3 | 7
0 | 1
2 | k
A.k = -2, y = -3x + 1
B.k = -3, y = -2x + 1
C.k = 3, y = 2x + 1
D.k = -5, y = -x + 1
Challenging
A line passes through the point (-6, -7) and has a slope of 3/2. Although you don't have a graph, you can create a table to find the equation. What is the equation of the line?
A.y = (3/2)x - 2
B.y = (3/2)x - 16
C.y = (3/2)x + 2
D.y = (2/3)x - 3
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