Equation of a Straight Line Worksheets
We begin this topic by helping students understand is a linear relationship exists within an equation and function. This is more of a real-world skill that we feel is important for students to fully grasp. There are number of different methods that use to explain linear and nonlinear equations to students. In most cases, we will present them through graphs, but they should also be comfortable with the algebra that it is rooted in. We also present function tables for students to work with. Students should understand the anatomy of an equation for a straight line. If you need a bit of a refresher on the anatomy of this equation, take a look at the bottom of the page where we fully explain it for you. These worksheets and lessons help students understand how to determine the equation of a line from given points that exist on the line.
Aligned Standard: Grade 8 Functions - 8.F.A.3
- Linear or nonlinear Step-by-Step Lesson- Graph the equations. If they are a straight line, we classify them as linear.
- Guided Lesson - This is a quick one because 2 out of 3 of the problems are visual. Problem 3 will ask you to make the graph first.
- Guided Lesson Explanation - Since the problems are mostly visual based, it makes them easier to explain.
- Independent Practice -You are on the hunt for linear equations. Graphs help out in a big way.
- Matching Worksheet - This is one of my favorite worksheets that I have ever made. Mostly because I put a lot of care into creating the graphs.
- Slope and Equation of Lines Five Pack - We describe a little bit about a line. We ask you to tell us more.
- Graphs & Equations of Lines Five Pack - I love how a simple line can be written as a formal equation.
- Equation of a Line Worksheet Five Pack - We focus on find the equations and their slopes.
- Answer Keys - These are for all the unlocked materials above.
I would be very surprised if students have a hard time with this after they complete all the homework sheets.
- Homework 1 - Determine if the function is linear or non-linear.
- Homework 2 - Linear- The equation must fit into the form y = mx + b The variables cannot have exponents. When graphed they must form a straight line.
- Homework 3 - The range of change is constant so the graph shows a straight line. Straight Lines = linear equations.
There is a ton of graphing in your future, if plan to tackle these problems.
- Practice 1 - Use the table to determine if the equation is linear or nonlinear.
- Practice 2 - Non-linear - Equations that do not graph as a straight line.
- Practice 3 - More work with data tables.
Math Skill Quizzes
I put two different sub-skills together with every sheet.
- Quiz 1 - Graphs and plotted points that help form a line image.
- Quiz 2 - Which function is linear?
- Quiz 3 - Plotted points with data tables.
What is the Equation of a Straight Line?
When it comes to analyzing just about anything mathematically, we are constantly looking to find multiple data points that result in a straight line or as close as possible to it. This is because a straight line indicates that a consistent and predictable relationship exists within those data sets. We can use this line that is created to make accurate forecasts and understand a set of clear expectations to be exhibited by our data.
Since the concept is broad, you can determine the equation of a straight line in the following forms:
y = m x + b
The y and x portions of this equation indicate an ordered pair. If you plug one of these variables into the equation, you will be able to determine the value of the other variable and determine a value for an order pair or point on this line. The m variable indicates the slope of the line. The slope tells us how steep it is. The b portion is called the y-intercept. This is the position of y value of the line when the value of x is equal to 0.
Using this simple format, we can learn a great deal about the lines that they create and the relation of that data that it took to compose this.
(y - y1)/(x-x1) = m, this is used when we have the slope of the line, m, and one-point given such as P1 = (x1, y1) through which the line crosses. The above equation is written in a form that makes it clear that both the given point P1 and slope of the line calculated at any point (x, y) are the same. The relationship is further simplified as: y = m (x-x1) + y1
The above-written form is simpler and tidier but doesn't reveal the truth about how the equation was derived. Slope: m = (y2- y1)/ (x2-x1); as the line crosses two different points (x1, y1) and (x2, y2), find out the slope of the line first to proceed.