A linear equation is also known as the one-degree equation because it has the highest degree as 1. The standard linear relations between x, y is ax + by + c = 0 where a, b, c are the real numbers and x, y are variables of the given equation. The graph of a linear equation with variables x and y forms a straight line.

Let us discuss how to draw the graph of standard linear relations between x, y from this article. For better understanding, we have provided examples of problems on the graph of standard linear relations between x, y. By this, the students who are lagging in the concept of coordinate geometry can score good marks in the exams.

## Quadrants and Convention for Signs of Coordinates

A graph has four quadrants. In quadrant 1 the values of x and y are positive, in Quadrant 2 the x variable value is positive and y variable value is negative, in Quadrant 3 the x variable value and y variable value is negative and in Quadrant 4 the x variable value is negative and y variable value is positive.

- Quadrant I – (+, +)
- Quadrant II – (+, -)
- Quadrant III – (-, -)
- Quadrant IV – (-, +)

Students of 9th Grade Math can make the most out of the concepts related to Linear Equations, Coordinate Geometry, Probability all under one roof.

### Linear Equation in One Variable

A linear equation with one variable has only x value. The equation of the linear equation in one variable is ax + b = 0 where a and b are the real numbers and x is the variable.

Example: Solve the linear equation in one varible 2x + 5 = 17.

Solution:

Given the linear equation 2x + 5 = 17

2x = 17 – 5

2x = 12

x = 12/2

x = 6

See More: Problems on Linear Equation in One Variable

### Linear Equation in Two Variable

An equation with two variables has ordered pairs x and y. Substitute the values of x and y to get the ordered pairs to plot the points on the graph.

X variable value |
X + 6 = y |
Y value |
Ordered Pair (x, y) |

-2 | -2 + 6 = y | 4 | (-2,4) |

-1 | -1 + 6 = y | 5 | (-1,5) |

0 | 0 + 6 = y | 6 | (0, 6) |

1 | 1 + 6 = y | 7 | (1, 7) |

2 | 2 + 6 = y | 8 | (2, 8) |

### Examples on How to draw Graph of Standard Linear Relations between x, y

**Example 1.**

Draw the graph of the linear equation in two variables y = 2x + 3.

**Solution:**

Given equation is y = 2x + 3

In the given equation

If x = -2 then y = 2(-2) + 3 = -4+3 = 1

If x = -1 then y = 2(-1) + 3 = 1

If x = 0 then y = 2(0) + 3 = 3.

If x = 1 then y = 2(1) + 3 = 5.

If x = 2 then y = 2(2) + 3 = 7

Plot the graph using the points (-2,1), (-1,1), (0,3), (1,5) and (2,7).

**Example 2.**

Draw the graph of the linear equation in two variables x − y = 2

**Solution:**

x – y = 2

– y = 2 – x

y = x – 2

If x = 0 then y = 0 – 2 = -2

If x = 1 then y = 1 – 2 = -1

If x = 2 then y = 2 – 2 = 0

If x = 4 then y = 4 – 2 = 2

Then plot the following points in the graph.

X | 0 | 1 | 2 | 4 |

y | -2 | -1 | 0 | 2 |

Example 3.

Draw the graph of the linear equation in two variables y = 4x + 1.

**Solution:**

Given equation is y = 4x + 1

In the given equation

If x = -5 then y = 4(-5) + 1 = -20+ 1 = -19

If x = -1 then y = 4(-1) + 1 = -3

If x = 0 then y = 4(0) + 1 = 1.

If x = 1 then y = 4(1) + 1 = 5.

If x = 2 then y = 4(2) + 1 = 9

Plot the graph using the points (-5,-19), (-1,-3), (0,1), (1,5) and (2,9).

**Example 4.**

Draw the graph of the linear equation in two variables 2x – 3y + 1 = 0

**Solution:**

Given equation is 2x – 3y + 1 = 0

2x + 1 = 3y

y = 2x + 1/3

In the given equation

If x = -1 then y = 2(-1) + 1/3 = -1/3

If x = 0 then y = 2(0) + 1/3= 1/3

If x = 1 then y = 2(1) + 1/3 = 1

If x = 2 then y = 2(2) + 1/3 = 5/3

Plot the graph using the points (-1,-1/3), (0,1/3), (1,1), (2,5/3).

**Example 5.**

Draw the graph of the linear equation in two variables x + y = 4

**Solution:**

x + y = 4

– y = x – 4

y = -x + 4

If x = 0 then y = 0 + 4 = 4

If x = 1 then y = -1 + 4 = -3

If x = 2 then y = -2 + 4 = 2

If x = 4 then y = – 4 + 4 = 0

Then plot the following points in the graph (0,4), (1,-3), (2,2) and (4,0)

### FAQs on Graphing Standard Linear Relations between x, y

**1. How do you graph X or Y?**

To plot a graph using an equation, first, we construct a table using the two values of x and y by substituting the values of x and y in the equation starting from 0 to so on. Then draw the points on the graph using the x and y values then values of x lie on the x-axis and the values of y lie on the y-axis.

**2. What type of graph is XY?**

Suppose we have an X-Y Plot. X-Y plots are used to determine the relationships between the two different things. The x-axis is used to measure one variable and the y-axis is used to measure the other variable. If both variables increase at the same time then they have a positive relationship.

**3. Which graph has a straight line?**

A linear graph has a straight line. It means if any relation gives a single straight line then it is a linear graph. The “linear” stands for a straight line.