Math 8a- unit 7 lesson 12 graphing linear equations
Lesson 12: Graphing Linear Equations
In this lesson, we will learn how to graph linear equations.
A linear equation is an equation in which the highest power of the variable is 1. It can be written in the form y = mx + b, where m is the slope of the line and b is the y-intercept.
To graph a linear equation, follow these steps:
Step 1: Find the y-intercept (b)
The y-intercept is the point where the line intersects the y-axis. To find the y-intercept, set x = 0 in the equation and solve for y.
Step 2: Find the slope (m)
The slope tells us how the line is slanted. It can be found by comparing the rise (change in y) and run (change in x) between any two points on the line. The formula for slope is: m = (y2 - y1) / (x2 - x1)
Step 3: Use the y-intercept and slope to plot more points
Using the y-intercept and slope, you can plot more points on the line. To do this, choose a value for x and substitute it into the equation to find the corresponding y-value. Plot these points on the graph.
Step 4: Draw the line
Once you have plotted several points, draw a line through them to represent the linear equation.
Example:
Let's graph the equation y = 2x + 3.
Step 1: Find the y-intercept (b)
Set x = 0:
y = 2(0) + 3
y = 0 + 3
y = 3
So the y-intercept is (0, 3).
Step 2: Find the slope (m)
Compare any two points on the line. Let's use the y-intercept (0, 3) and another point (2, 7):
m = (7 - 3) / (2 - 0)
m = 4 / 2
m = 2
So the slope is 2.
Step 3: Plot more points
Using the y-intercept and slope, we can plot more points on the line. Let's choose x = 1 and substitute it into the equation:
y = 2(1) + 3
y = 2 + 3
y = 5
So another point on the line is (1, 5).
Step 4: Draw the line
Now that we have several points, we can draw a line through them.
The graph of y = 2x + 3 is a straight line that passes through the points (0, 3), (1, 5), and (2, 7).
Remember to label the axes and title the graph to make it clear and presentable.