Math 8 A - Unit 7, Lesson 12: Graphing Linear Equations
In this lesson, you will learn how to graph linear equations. A linear equation is an equation in which the variables have an exponent of one. The graph of a linear equation is a straight line.
To graph a linear equation, you need to determine two points on the line. The easiest way to find two points is to set the x-value to zero and find the corresponding y-value, and then set the y-value to zero and find the corresponding x-value. Once you have these two points, you can draw a straight line through them.
For example, let's graph the equation y = 2x + 3. To find the first point, we set x = 0 and solve for y. Plugging in x = 0 into the equation, we get y = 2(0) + 3, which simplifies to y = 3. So our first point is (0, 3).
To find the second point, we set y = 0 and solve for x. Plugging in y = 0 into the equation, we get 0 = 2x + 3. Subtracting 3 from both sides, we get -3 = 2x. Dividing both sides by 2, we get x = -3/2. So our second point is (-3/2, 0).
Now we can plot these two points on a graph and draw a line through them. The graph of y = 2x + 3 is a straight line with a slope of 2 and a y-intercept of (0, 3).
In addition to graphing linear equations, you can also determine the slope of a linear equation. The slope is the ratio of the vertical change (change in y) to the horizontal change (change in x) between two points on the line.
For example, in the equation y = 2x + 3, the coefficient of x is 2. This means that for every one unit increase in x, y increases by two units. So the slope of this line is 2.
You can also determine the y-intercept of a linear equation, which is the point where the line intersects the y-axis. In the equation y = 2x + 3, the y-intercept is (0, 3), as we found earlier.
Graphing linear equations can help you visualize the relationship between the variables in the equation. It can also help you find the solution, or point of intersection, between two linear equations.