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Point Slope Form

8.F.B.4
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Grade 8 Functions - 8.F.B.4

There are three different methods that are commonly used to write the equation of a line (linear equation): general form, slope-intercept, and point slope form. We are very familiar with the slope-intercept form because it makes it simple to draw precise lines in a coordinate plane. The point slope form is used much more in algebraic settings rather than graphically setting. This is because it provides exact locations (points) of the line. Writing equations in this form usually indicates that we are comparing lines or trends in some way. This form lends itself to producing math that is easier to work with in this regard. These worksheets and lessons put you in apposition to be a detective. By using the point slope form you answer questions about lines.

Printable Worksheets And Lessons






Homework Sheets

We describe a line- you tell us the equation for that line.

  • Homework 1 - A line has a zero slope and passes through the point (-3, 5). What is the equation of the line?
  • Homework 2 - Find the slope of the line that passes through (2, 3) and (9, 5).
  • Homework 3 - A line has a slope of 2 and passes through the point (-3, 5). What is the equation of the line?



Practice Worksheets

The descriptions of the lines are all over the place.

  • Practice 1 - A line has a 2 slope and passes through the point (3, 2). What is the equation of the line?
  • Practice 2 - Find the equations of the lines that are described.
  • Practice 3 - More line equations for you to conjure up.



Math Skill Quizzes

You will be surprised how quickly kids pick up this skill.

  • Quiz 1 - Find these lines with fractional slope values.
  • Quiz 2 - This is the quiz that will test it for you.
  • Quiz 3 - Find the slope of the line that passes through (2, 3) and (4, 7).

What is Point Slope Form?

We you are working with coordinate graphs you will learn more about the mathematical concepts and you will come to understand that this form of mathematics features a broad array of concepts. One such broad mathematical concept is the concept of linear equations. The concept of linear equations is not just broad but also a tad bit complex to comprehend. They are algebraic equations between two variables (x, y) which when plotted on a graph create a straight line.

There are three different ways to represent or write a linear equation.

1. General form- ax + by + c = 0 (here both a and b have to be a non-zero number)

2. Slope-Intercept- y = mx + b, this is the most common form of linear equation, where m represents the slope (steepness) of the line and the variable b indicates the point where the line crosses the y-intercept. Having those two features pointed out makes it much easier than the other forms to draw an accurate line. Which is why this is a very popular method.

3. Point-slope form- (y - y1) = m(x - x1)

We use this form of writing linear equations when of at least one point on the line and the slope of the line. A point-slope equation is a linear equation that has a point (x1, y1) and a slope m. The entire equation focuses on the point on the line and the slope of the line. This linear equation is derived from the other equation can be used for finding the slope of a line. We tend to use this form more when we are tracking comparisons between multiple lines or trends on a graph. This method often produces algebra that is easier to solve.