Slope

The slope of a line is a measure of how steep the line is. It is represented by the letter "m" in the equation of a line: y = mx + b, where m is the slope and b is the y-intercept.

Calculating Slope

The slope of a line can be calculated using the formula:

m = (y₂ - y₁) / (x₂ - x₁)

(x₁, y₁) and (x₂, y₂) are two points on the line.
Substitute the coordinates of the two points into the formula to find the slope.

Interpreting Slope

The slope of a line can be interpreted as follows:

If the slope is positive, the line slants upwards from left to right.
If the slope is negative, the line slants downwards from left to right.
If the slope is zero, the line is horizontal.
If the slope is undefined, the line is vertical.

Practice Problems

Calculate the slope of the following lines:

Line 1: (3, 5) and (7, 11)
Line 2: (-2, 4) and (-2, -3)
Line 3: (1, 2) and (1, 6)

Graphing Lines with Slope

To graph a line using its slope, start by plotting the y-intercept (the point where the line crosses the y-axis). Then, use the slope to find additional points on the line by moving up or down and to the right from the y-intercept. Connect the points to graph the line.

Be sure to check your understanding of the material and practice calculating slope with additional problems to reinforce your learning!

◂Math Worksheets and Study Guides Sixth Grade. Volume

The resources above cover the following skills:

Geometry (NCTM)

Use visualization, spatial reasoning, and geometric modeling to solve problems.

Use geometric models to represent and explain numerical and algebraic relationships.

Measurement (NCTM)

Apply appropriate techniques, tools, and formulas to determine measurements.

Select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision.

Develop strategies to determine the surface area and volume of selected prisms, pyramids, and cylinders.

Connections to the Grade 6 Focal Points (NCTM)

Measurement and Geometry: Problems that involve areas and volumes, calling on students to find areas or volumes from lengths or to find lengths from volumes or areas and lengths, are especially appropriate. These problems extend the students' work in grade 5 on area and volume and provide a context for applying new work with equations.