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Graphing Equations

Answer Keys Here

Aligned To Common Core Standard:

High School - HSA-CED.A.2

How to Graph Equations? Graphing equations is one way of solving simultaneous linear equations. If you are looking for easy ways to find the solution to a set of linear equations, graphing the equations is the best option. It is easy, simple, and can be done in just a few short steps. Step 1: Substitute 0 in place of x - The first step is to substitute the x-variable with zero and find out the corresponding value of y. It is the y-intercept of the line. Step 2: Substitute 0 in place of y - The next step is to substitute the y-variable with zero and find out the corresponding value of x. It is the x-intercept of the line. Step 3: Plot the Coordinates - The third step is to plot the coordinates on the graph. The coordinate pairs that you calculated by substituting 0 in place of y and then in place of x. Step 4: Draw a Straight Line - Connect the plotted points with a straight line. To graph any linear equation start by finding the point of the y-intercept and drop a point there. Take the slope and use it to find a second point. Then just draw a line that connects those two points.

Printable Worksheets And Lessons

  • Simple Equations Step-by-step Lesson- We start with the most basic setup possible.

  • Guided Lesson - We stick with the basics to make sure students have a solid handle on it.

  • Guided Lesson Explanation - If you notice, all of these equation have a very close slope to help students understand the concept. This can lead to further discussion.

  • Practice Worksheet - I threw some negatives in here just to add a slight bit of a challenge for them.

  • Matching Worksheet - Find the matching graph for each equation. I find that students really start to grasp the concept well with this type of worksheet.

Homework Sheets

The focus here is just worrying about the intercepts.

  • Homework 1 - The x-intercept is where the line touches the x-axis (left to right). The y-intercept is the y-coordinate of the point where the graph crosses the y-axis.
  • Homework 2 - The x-intercept where y = 0 and solve for the x-intercept.
  • Homework 3 - We draw the two intercepts on a graph and let a straight line pass straight through them.

Practice Worksheets

Using this format will really make the concept sink in quicker.

  • Practice 1 - Mark a line between the two intercepts. You would be amazed what can come from two variables and a constant.
  • Practice 2 - Graph functions below using intercepts: x + y = 10. When you are done, you will have ten lines in all.
  • Practice 3 - Graph the equation below by using their intercepts. You might need some extra paper for these because the constants are large.
  • Practice 4 - You will make a graphic for each problem. Example exercise: x + y = -16

Math Skill Quizzes

The quizzes should be doable to give them confidence.

  • Quiz 1 - Graph the equation below by using their intercepts. x + y = 21
  • Quiz 2 - Bring any of your thoughts through this process.
  • Quiz 3 - Watch out for the negative numbers. Do not let them throw you off the trail.

More Lessons

Since this could be a really challenging topic for many students I added more lessons.

  • Extra Lesson - We just begin to drop numbers into the equation and create our line. Choose random values for x and see what you get for y when you plug it into the equation.
  • Another Matching Sheet - Match the word problems to their answers. Write the letter of the answer that matches the problem.
  • Guided Lesson 2 - Graph the following equations.
  • Guided Explanation 2 - The slope means m of this line- its steepness, or slant- can be.

Why Is This Skill Important?

When you are trying to understand just about anything images come in handy to give you an instant picture of the situation. It is like driving on the and seeing a traffic sign, you suddenly grasp what you need to be aware of in your environment. Having a graphical representation of an equation really helps you understand the relationship of the data that passes through it. You can easily understand the constant nature of the data by understanding the value of the slope that it displays. Once you have a solid graph present you can quickly make predictions that are highly accurate. If the graph is linear, you can comprehend what conditions it satisfies. This is a skill that is highly valued in the corporate world. Some of the most highly compensated career regularly use this skill to make well thought out business decisions.