Graph quadratic equations, system of equations or linear equations with our free step-by-step math calculator. The real importance of emphasizing graphing linear equations with your students, is that they should already know that any two points determine a line. This video shows how to graph linear equations from the standard form of a linear equation and also the.


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Let's feed it a few values for x and see where y goes. A favorite value for x is 0, so let's start there.

Linear Equations

All right, let's give it another value for x, perhaps 5, and graphs of linear equations where that takes us. Take a look at Figure 2. Notice that A 0,0 is the origin because both it's x and y values are 0. For B 1,2the x value would be 1 and the y value would be 2.

To plot the point, we would go graphs of linear equations the positive direction on the x axis until we hit 1, then we would go up on the positive y axis until we hit 2. This is where the point is located. We get our points by just lining up the x value and y value to get their locations, and we can do this for any coordinate pair.

Horizontal and Vertical Lines On the coordinate plane, we know that each point must have an x and a y value.

When we solved equations in one variable, it was easy to see that we had an x value. What we didn't realize is that we also had a y value as well. In fact, we had infinitely many y values.

Similarly, graphs of linear equations we were to solve a one variable equation in terms of y, we would have infinitely many x values.

These equations do not form a point, but rather a horizontal or vertical line. When x equals a number, y can take on any value and it would not change the equality.

We could think of the equation as having a y value with 0 as a coefficient, so no matter what value y takes, it will always multiply by 0. This will form a vertical line. Similarly, when y equals a number, x can take on any value and it would not affect the graphs of linear equations.

Linear equations in the coordinate plane

We could think of the equation having value of 0x, so x graphs of linear equations be any number and it would not affect the equation. This graph will be a horizontal line. Solutions of Equations in Graphs of linear equations Variables We have seen expressions and equations of one variable, mainly x.

Here is an expression When we plug in different values of x, we also yield a different output as well.

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Since this output varies depending on x, we can also use a variable to represent graphs of linear equations output of x. When dealing with equations in two variables, the solutions graphs of linear equations of x and y values that make the equation true when plugged into the equation.

Thus, Example 1 Find the slope of the line containing the two points with coordinates -4, 2 and 3, 5 as shown in the figure at the right. Solution We designate 3, 5 as x2, y2 and -4, 2 as x1, y1. Substituting into Equation 1 yields Note that we get the same result if we subsitute -4 and 2 for x2 and y2 and 3 and 5 for x1 and y1 Lines with various slopes are shown in Figure 7.


Slopes of the lines that go up to the right are positive Figure 7. And note Figure 7. However, is undefined, so that a vertical line does not have a slope.


In this case, These lines will never intersect and are called parallel lines.

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