Equations of a line can take multiple forms, with variations in appearance, but each describing the same line in a linear equation. One such form is the slope intercept form:
Most commonly stated, the formula is: y = mx + b
- m = slope of the line
- b = y-axis intercept of the line
Slope intercept form is the most commonly used form of linear equations, where the coefficients utilized in the equation represent the slope and line intercept, hence the name of the form as the slope-intercept form.
Making the Calculation
There are many on-line tools available where you simply enter the values/points of your equation, and generate the equation and results quickly.
The results provided by these slope intercept form worksheets include the slope and the y-intercept of the line described by the values you provide on the worksheet.
The issue – you must first arrive at the coefficients to be entered on the worksheets, with a precise level of accuracy. To find the slope intercept, you must provide the coordinates for each of two points.
With Algebra students particularly in mind, Math-Aids.com provides a set of worksheets valuable for solving a variety of linear equations. These include worksheets for:
- Calculating slope from a graphed line
- Solving the slope value from a pair of points provided
- Using a linear equation to find the y-intercept and slope
- Graphic lines in slope intercept form
Certainly, there are other ways to solve slope intercept equations, through the use of a scientific graphing calculator.
Let Your Calculator do the Work
With a scientific calculator, slope calculations become a breeze. With the coordinates provided on your graphs, solving linear equations in slope intercept form can be as simple pushing a few buttons.
- Texas Instruments’ family of graphing calculators are examples of slope intercept form calculators that can accomplish such linear equations quickly and accurately. TI works with educators to reinforce the importance of mathematics in education with specialized programs that include the application of TI graphing calculators in the classroom.
Activities include applying Algebra and Geometry to solve complex problems, utilizing TI calculators such as the TI 83/84 models, TI Nspire, and TI 89 Titanium graphing calculators.
Professionals may want to invest in TI’s truly high-powered top-of-the-line Nspire CX CAS graphing calculator. This unit not only provides notation and algebraic expressions for entering values, but provides tools for data analysis and hypothesis testing. Want to enter some notes with your data? This one is for you. Enter on-screen instructions and other pertinent information right along with your data, to keep everything organized and together.
TI is not alone in providing the technology that enables both students and professionals to solve linear equations such as slope intercept form problems.
- Casio offers an economical option for a graphing calculator in the FX-9750GII. This relatively inexpensive device offers an easy-to-use user interface, a high-resolution display, and powerful processor. USB connectivity makes it a snap to connect to other calculators or your PC or laptop computer. It also features a one-step feature for solving graph problems.
Take a step up on the Casio line, and the FX-CG10 PRIZM will provide additional features such as larger keys to avoid typos and simplified navigation – perfect for students.
- HP has always had a good handle on high-tech and scientific equipment, and their G8X92AA LA Prime graphing calculator is no exception. This calculator is packed with features that include a color touch-screen along with keypad entry, long-life rechargeable battery, and a variety of available applications to tailor the calculator for your needs. Switch between numerical and symbolic views with the touch of a button.
Note that each of the manufactures/models listed here receive high ranks from reviewers and users. There are many others available on the market that may also suit your specific needs for graphing, connectivity to other devices, or unique features that drive your decision.
Why is Slope-Intercept Form Important?
There are many real-life applications for determining these values:
- Construction applications for evaluation of materials and equipment required for a project
- Aviation – planning flight paths and take-off/landing approaches
- Recreation – experienced mountain climbers and guides utilize such technology in planning climbs and determining the best routes to be taken
These are just a few examples that illustrate why slope intercept is not just a math exercise or something to do with your calculator when you’re bored.
Slope intercept form is a standard solution for solving linear equations. While there are numerous applications on the internet that provide slope intercept form worksheets that are useful, nothing beats having your data, graph, and solutions in the palm of your hand.
Feature image via Tes