Mathematics
Grade 7
15 min
Graph a line from an equation
Graph a line from an equation
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify a linear equation.
Create a table of values for a given linear equation.
Plot ordered pairs on a coordinate plane.
Connect plotted points to form a straight line.
Accurately graph a line from its equation.
Understand that every point on the line is a solution to the equation.
Have you ever seen a straight path or a road on a map? 🗺️ What if we could draw those paths using math?
In this lesson, you'll learn how to take a simple mathematical rule, called an equation, and turn it into a straight line on a graph. This skill helps us visualize relationships between numbers and understand how things change together.
Real-World Applications
Tracking the distance traveled over time at a constant speed.
Calculating the cost of items based on...
2
Key Concepts & Vocabulary
TermDefinitionExample
Linear EquationAn equation that, when graphed, forms a straight line. It shows a relationship where a change in one variable causes a proportional change in another.`y = x + 3` or `y = 2x - 1` are examples of linear equations.
Coordinate PlaneA two-dimensional surface formed by two perpendicular number lines, the x-axis (horizontal) and the y-axis (vertical), used for plotting points.The grid paper you use for graphing is a coordinate plane.
Ordered PairA pair of numbers `(x, y)` that gives the location of a point on the coordinate plane. The first number is the x-coordinate, and the second is the y-coordinate.The point `(2, 5)` means you move 2 units right from the origin and 5 units up.
x-axisThe horizontal number line on the coordinate plane. It represents the ind...
3
Core Formulas
Rule for Finding Solutions (Points)
For an equation like \( y = ax + b \) or \( x + y = c \), choose several values for \( x \), substitute them into the equation, and calculate the corresponding \( y \) values to get ordered pairs \( (x, y) \).
This rule helps you find specific points that lie on the line. At least two points are needed to draw a line, but finding three or more helps ensure accuracy.
Rule for Plotting Points
On a coordinate plane, start at the origin \( (0,0) \). Move \( x \) units horizontally (right for positive, left for negative) and then \( y \) units vertically (up for positive, down for negative) to mark each point.
This rule guides you on how to correctly place each ordered pair you found from the equation onto the graph.
Rule for Drawing the Li...
4 more steps in this tutorial
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Challenging
A straight line on a coordinate plane passes through the point (2, 7). Which of the following equations could represent this line?
A.y = 2x + 2
B.y = x + 4
C.y = 4x - 1
D.y = 7x - 2
Challenging
The points (1, a) and (3, 11) are both on the line graphed from the equation y = 3x + 2. What is the value of 'a'?
A.5
B.3
C.6
D.2
Challenging
A student is graphing y = (1/2)x + 1. They choose x-values of 0, 1, and 2. Why might choosing x-values of 0, 2, and 4 be a better strategy?
A.Using larger numbers is always better.
B.Odd numbers don't work in equations with fractions.
C.The points will be closer together and easier to connect.
D.Using even numbers for x will result in whole numbers for y, which are easier to plot.
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