Online Linear Equation Graph Calculator
How to use the linear equation graph calculator?
- Start off by entering the linear equation into the given input field.
- Click on “Solve” to obtain the result.
- Finally, the output field will display the x-intercept and the y-intercept of the equation.
- You can check “Show steps” to understand the steps followed to get the answer.
- Analyze the graph to understand how the coordinates have been plotted.
- Also explore more by clicking “Example” to view various equations and their corresponding graphs.
What is a linear equation ?
A linear equation is defined as an equation with a degree of one. When this equation is graphed, we can see that it will always take the shape of a straight line.
What is a linear equation in one variable ?
A linear equation in one variable is a single-variable equation. Ax + B = 0 is the standard form of a linear equation in one variable where x is the variable, A its coefficient, and B is a constant in this equation.
What is a linear equation in two variable ?
A two-variable equation is called a linear equation in two variables. A linear equation in two variables written in the standard form is Ax + By = C where x and y are variables, A and B are coefficients, and C is a constant.
What is the solution of an equation? How are they represented on a graph?
A solution is a value or a set of values when substituted for the unknown, makes the equation true.
Each value or set of values will act as a point on the line of the graph. This means that each ordered pair of that line is a solution of the equation.
What is x-intercept?
The x coordinate of the point at which a line crosses the x-axis is the x intercept. On the x axis there is no y coordinate. Hence, to find the x intercept of an equation without drawing the graph, we just need to substitute the value of y as zero, the resulting x value is the x intercept.
Solved Examples
Example 1: Solve the equation 3x + 9 = 0
Solution:
Step 1: Make a table of values.
x | y = 3x + 9 | y | (x, y) |
|---|---|---|---|
-1 | y = 3(-1) + 9 | 6 | (-1, 6) |
0 | y = 3(0) + 9 | 9 | (0, 9) |
1 | y = 3(1) + 9 | 12 | (1, 12) |
Step 2: Plot the ordered pairs.
Step 3: Now through these points, draw a straight line.
Example 2: Draw the graph of y = 2x + 4
Solution:
Step 1: Make a table of values.
x | y = 2x + 4 | y | (x, y) |
|---|---|---|---|
-1 | y = 2(-1) + 4 | 2 | (-1, 2) |
0 | y = 2(0) + 4 | 4 | (0, 4) |
1 | y = 2(1) + 4 | 6 | (1, 6) |
Step 2: Plot the ordered pairs.
Step 3: Now through these points, draw a straight line.
A mathematical expression containing the equal symbol is known as an equation.
When a line intersects another line we get a point of intersection. So, when a line intersects the y-axis we obtain a point of intersection. The y coordinate of this point is called the y-intercept.
To solve for all the variables, we need an equal number of equations as the variables. So we cannot solve an equation with two variables using only one equation. But in a single equation, if we have the value of one variable then the value of the other variable can be found.
To show the relationship between data items, tables of values are used. To plot graphs, we create a table of values. This table shows the values of the y coordinate for particular values of the x coordinate. Hence ordered pairs are found, which are plotted. These points are joined to create the graph of that equation. Hence creating the table of values is an important step in drawing the graph of an equation.
On the y-axis, we know that there are no x coordinates. Hence, x = 0 is the general form of the y-axis equation.