Graphing Linear Equations
Graphing Linear Equations is one of the most crucial concepts of algebra. A linear equation is an equation of degree one, which means that the exponents of variables in a linear equation can only be 1, not greater than 1 in any of the cases. Linear equations can be in one as well as two variables. Solving a linear equation is to find the value of variables contained in it and the graphical method is one of the methods to solve linear equations, either one or two variables linear equations.
|1.||What Is Graphing Linear Equations?|
|3.||Solved Examples on Graphing Linear Equations|
|4.||Practice Questions on Graphing Linear Equations|
|5.||FAQs on Graphing Linear Equations|
What Is Graphing Linear Equations?
Linear equations are algebraic equations in which each term has a real constant and the equation contains 2 variables of the highest power 1. We represent the linear equation in y=mx+b form, also known as the y-intercept form. The representation of a linear equation on a graph is called graphing linear equations. Let us see an example of graphing a linear equation. We have to represent the equation x+2y=7 in a graph.
Here, the equation x+2y=7 makes a straight line on the graph. Similarly, all linear equations create a straight line on the graph.
- The point where any line crosses the x-axis on the graph - X-intercept
- The point where any line crosses the y-axis on the graph - Y-Intercept
Graphing Linear Equations
Graphing a linear equation is about solving the linear equations and the solution of the linear equation can be represented in a coordinate plane. Following steps are to be taken up:
- Make sure the linear equation is in y-intercept form, which is y = mx + b.
- Apply the trial and error method and find the value of (x, y) up to three pairs, which satisfy the linear equation.
- Find the x-intercept and y-intercept of the equation. For y-intercept, substitute the value of x = 0 in the equation. This results in x = a, for x-intercept, substitute the value of y = 0 in the equation. This results in y = c.
- Thus, the points are (a, 0) and (0, c). Make a tabular form and put the value of x and y respectively.
- Plot all the points on the graph paper.
- Join all the points which are marked on the graph and you will get a straight line representing the given linear equation graphically.
Example: Draw a graph of the linear equation x+2y=7.
We will follow the following steps:
- Step 1: Check if the given linear equation x+2y=7 is of the form of y = mx + b. [On converting, we get: y = - (1/2) x + 7/2]
- Step 2: Find the x and y-intercept respectively. For that, put y = 0 in the equation: x = 7-2(0), x=7. Now, put x=0 in the equation. 2y=7-(0), y=7/2 = 3.5
- Step 3: Apply the trial and error method and find 3 pairs of values of (x, y) that satisfy the given linear equation x=7-2y. (See table below)
- Step 4: Plot the points (7,0), (5,1), and (3,2) on the graph.
- Step 5: Join all the points which are marked on the graph paper and get a straight line that represents the given linear equation graphically.
See the values of x and y in the following table:
- Linear equation in two variables has infinitely many solutions.
- The graph of linear equation is always a straight line.
- The equation y = mx is always passing through the origin (0, 0).
- The sum of the digits of a two-digit number is 8. When the digits are reversed, the number is increased by 18. Find the number.
- Jake's piggy bank has 11 coins (only quarters or dimes) that have a value of $1.85. How many dimes and quarters does the piggy bank have?
Topics Related to Graphing Linear Equations
Solved Examples on Graphing Linear Equations
Example 1: Isabella has the linear equation x - 2y = 2. Help her to draw the linear equation on the graph.
The given linear equation is x-2y=2. Convert the equation in the form of y = mx + b⇒ y= x/2 - 1. We need to find the x and y-intercept respectively. For that, put y=0 in the equation⇒ x=2(0)+2, x=2. Now, put x=0 in the equation. 2y=(0) - 2, y=1. Now, we will apply the trial and error method, and find 3 pairs of values of (x, y) that satisfy the given linear equation y=x/2-1. See the values of x and y in the following table:
x 2 4 0 y 0 1 -1
Plot the points (2,0),(4,1),(0,-1) on the graph. Join all the points which are marked on the graph paper and get a straight line that represents the given linear equation graphically.
Example 2: William wants to plot the graph of -1/2x+1/3y=1. Help him to plot the graph for linear equations.
The given linear equation is -1/2x+1/3y=1. Convert the equation in the form of y = mx + b⇒ 6 + 6x/2. We need to find the x and y-intercept respectively. For that, we can apply the hit and trial method, put y=6 in the equation⇒ x=3. Now, put x=2 in the equation. y=3. See the values of x and y in the following table:
x 2 0 y 6 3 Solutions (2,6) (0,3)
FAQs on Graphing Linear Equations
How Do you Graph a Linear Equation?
The basic methods of the graphing linear equation:
- The first method is by plotting all points on the graph and then drawing a line through the points.
- The second is by using the y-intercept of the equation and slope of the equation.
What Are the 3 Ways to Graph a Linear Equation?
The 3 ways to graph a linear equation:
- Using two points to plot the graph of a linear equation.
- Use the slope and y-intercept of a linear equation.
- Using the x- and y-intercepts of a linear equation.
How Do you Graph a Linear Equation with Two Points?
Graphing linear equation with two points:
- Find the y-intercept from the linear equation and plot the point.
- From the y-intercept of the linear equation, use the slope to find the second point and plot it on the graph.
- Draw a straight line to connect the two points on the graph.
What Is the Formula For a Linear Equation?
The formula for a linear equation is y = mx + b.
How Do you Graph a Linear Equation Using Intercepts?
To find intercepts algebraically, we use the fact that all x-intercepts have y=0 and all y-intercepts have x=0.
Determine the corresponding values of x and y by putting the values of x-intercepts and y-intercepts respectively.
What Is the Minimum Number of Points Needed to Graph a Linear Equation?
Two points are the minimum number of points needed to graph a linear equation
How Do you Find the Y-Intercept of a Graph?
The y-intercept of a graph is the point at which the graph crosses the y-axis and at y point, the x-coordinate is zero.
How Do you Find the Intercepts of a Graph?
First of all, an equation must satisfy ax+by=c. Then you just set x = 0 to find the y-intercept and set y = 0 to find the x-intercept. Then find the corresponding values.