## Graphing Linear Equations

#### Aligned To Common Core Standard:

**High School** - HSA-CED.A.2

A linear equation is just a fancy way of say an equation for a straight line. In science they serve a particularly important purpose and are one of the foundational tools that scientists use to describe and identify relationships between two variables somewhere in the physical world. Once a relationship is identified it can be used to make accurate predictions of future interacts of those variables. This helps the scientific community explore the world and the complexity of the universe. These types of relationships are fairly common and can easily be gauged using a simple graph. There are positive relationships between variables that results from the line graph increasing (rises) from left to right. This means as one rises, so does the other. As you would think, negative relationships are ordinary too. They are sometimes referred to as inverse relationships and the line steadily falls on the graph, in this case. This selection of lessons and worksheets will help you understand an equation in linear form. They will review the concept of slope and intercepts.

### Printable Worksheets And Lessons

- Simple Equations Step-by-step Lesson- You are given an equation and we walk you through all the steps to bring it to life on a graph.
- Guided Lesson - We learn how to sketch lines, find the slope, and where it crosses the y-axis.
- Guided Lesson Explanation - We explain everything you need to know for this skill. This is three pages in all.
- Practice Worksheet 1 - You bring to life three instances of this on a single graph. A nice way to visualize how everything relates.
- Independent Practice 2 - You are only given the slope and the y-intercept and asked to pull everything out from that. A more advanced approach to this skill.

#### Homework Sheets

We hit this skill from every different angle. It really shows you the power of only having a small amount of information.

- Homework 1 - You will sketch six lines.
- Homework 2 - You will really break down the slope-intercept form.
- Homework 3 - Put all your math skills to work here. You will need to decide on fixed points of your own to work off of.

#### Practice Worksheets

As you pass over all these sheets, you should have a decent understanding of the nature of these types of exercises.

- Practice 1 - Do not get lost in all of threes and fours in here.
- Practice 2 - We introduce a few more fractions for you to work with.
- Practice 3 - You are given ordered pairs to determine the lines that they would create.

#### Math Skill Quizzes

The mastery of skill increases with each successive quiz. Yes, ironically there is a linear relationship behind this approach.

- Quiz 1 - Once you create the lines, go back and make sure it fits the slope and intercepts properly.
- Quiz 2 - You can pretty much choose any points to work off of from the lines. The more spread out that they are, the more accurate the line will be.
- Quiz 3 - The ordered pairs quiz that puts it all together for you.

### How Do You Graph These Guys?

You are given the linear equation: y = 4x – 6 and asked to plot the line on a graph.

**Logic:** If you want to creep in on the numbers that are involved within a linear equation, you can graph it by finding any two solutions such as (x1, y1) and (x2, y2) and just plot them on a graph, so why don’t we do that? To set this up so we could do it, just set the opposite variable to zero to solve for the other variable. We could proceed with x or y as 0, but why not start with x since it alphabetically comes first?

**Step 1: Set x to 0 in the equation.**

y = 4(0) – 6

y = -6

**Step 2: Set y to 0 in the same equation.**

0 = 4x – 6

6 = 4x

6/4 = x

1.5 = x

**Step 3: Review what we know already based on our first two steps.**

Reviewing step 1, we know one point on the line is (0, -6).

Reviewing step 2, we know another point on the line is (1.5, 0).

**Step 4: Plot the two points and connect them by drawing a line.**