# Graphing Linear Functions

Sub Topics

In Algebra 2 help ,A linear function with two variables is a variable function, that is, the value of one variable (called as dependent variable) varies with the values assigned to the other variable(called as independent variable). Usually the independent variable is denoted by the letter ‘x’ and the dependent variable is denoted by the letter ‘y’

The graph of a linear function is always a straight line. It is either a vertical line or a horizontal line for a linear function with single variable and an inclined line for a linear function with two variables.

Graph linear functions for the below questions and get practiced to similar kind of problems.

## Graph Linear Function with One Variable

This graph is from algebra answers where a Graph linear function with one variable is expressed either as x = a or, y = a, where ‘a’ is a constant.

The form, y = a, represents a horizontal line in a coordinate grid, parallel to x-axis and at a distance of ‘a’ units from x-axis. To draw a graph of this function, mark ‘a’ units on y-axis and draw a horizontal line passing through that.

Interestingly, the x-axis in a coordinate grid is represented by the linear function, y = 0 and the y-axis in a coordinate grid is represented by the linear function, x = 0

The form, x = a, represents a vertical line in a coordinate grid, parallel to y-axis and at a distance of ‘a’ units from y-axis. To draw a graph of this function, mark ‘a’ units on x-axis and draw a vertical line passing through that.

## Graphing Linear Function with Two Variables

Since the graph of a linear function is a straight line just two points are needed in a grid to draw the graph. First rewrite the function in slope intercept form, if it is in some other form.

Graphing linear function with two variables is all about ploting two points in the garph.

There are two methods to locate two points in the grid.

1) Mark the y-intercept of the given function. This is one point. Use the slope to construct the second point adjacent to the y-intercept. Now draw a line passing through these two points.

This method will be comfortable if the slope and y-intercept are compatible numbers.

2) By guess and check find two compatible ordered pairs. You can try a convenient number as input to get another convenient number as output. Plot these ordered pairs on the grid. Draw a line passing through these points.

This method can be followed if the slope and y-intercept are not compatible numbers.

Although two points are sufficient to draw the graph of a linear equation, you may be more comfortable by plotting additional points from an input-output table of the function.

We use the above methods in solving math problems of linear eqautions in 2 variables.

## Examples of Graphing Linear Function with Two Variables

Draw the graph for the function 2x + 4y = 6

The given function is rewritten as, 4y = -2x + 6 or, y = -(1/2) + 3

The y-intercept is 3.

The slope is -(1/2). That means for every two units of run, the fall is 1.

The graph is drawn as explained below.

## Problem on Graphing a Linear Function with Two Variables

Draw the graph for the function 3 x + 5y = 4

By guess and check, the value of y is (-1) for x = 3 and is 2 for x = -2

Plot two points with ordered pairs (3, -1) and (-2, 2).

Draw a line passing through these points.