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Writing Linear Equations

Graphing Review

Linear Equations

In prior lessons, you have learned many formulas.

In this lesson, we will represent the data (information as ordered paird) in a variety of ways: tables, graphs, equations in slope intercept form and standard form.

Key Concepts:

  • ordered pairs
  • tables
  • graphs
  • linear equations
  • slope intercept form
  • standard form

Table

In the last lesson you learned how to make an equation of a line in slope intercept form given two points on a line. The first objective for this lesson is very similar. You will be able to write the equation of a line in slope intercept form if you know more than two points on a line.

x y
-2 0
0 3
2 6
4 9
6 12

graph with points: A = (-2,0); B = (0, 3); C = (2, 6); D = (4, 9); E = (6, 12) and line connecting those points

Slope Intercept Form

Writing Equations From a Table of Values

We are now going to learn how to write the equation of a line from a table of values. If you understood how to do it with two points from last lesson then you will love this - it's the same process!

Since the slope of a line never changes, we will do just like before, which is to either graph the line to find our slope and y-intercept or find them algebraically. Except this time, if we decide to do it algebraically, we get to choose our own two points to work with from a table of values. So if you did well last lesson you will do well again and if you had some trouble then you get to have another opportunity to have a better understanding.

graph with line point A is at (0, 0) point B is at (6, 4); run is 3 and rise is 2

Example #1

Open Graph and Write the Equation of a Line in Slope-Intercept Form Using a Table of Values and Use the Equation to Solve a Real-World Problem in a new tab

Algebraic Approach

Finding the Equation Algebraically

See how much easier it is having an equation to solve future problems?

We obtained our equation from a graph but remember that we can also find it algebraically using the table of values.

x y
-2 0
0 3
2 6
4 9
6 12

graph with line connecting points: A = (2, 1); B = (4, 2); C = (6, 3); D = (8, 4); E = (10, 5)

Example #2

Open Write the Equation of a Line in Slope-Intercept Form Using a Table of Values in a new tab

Standard Form

Slope Intercept Form vs. Standard Form

Slope intercept form is easy to write if you have the slope and the y-intercept:

y = mx + b

This form is also nice if you want to graph the line.

However, many linear equations are written in standard form, which is:

Ax + By = C

You can't just look at the letters A, B, and C and quickly graph this line. You have to rewrite into slope intercept form.

To rewrite the linear equation from standard form to slope intercept form, you isolate the y-term (place the y-term by itself on the left side of the equation and make sure it has a coefficient of 1):

Ax + By = C

y = mx + b

Example #3

Open Rewrite the Linear Equation from Standard Form to Slope-Intercept Form in a new tab