Slope intuition

Slope intuition
Description
Exercise Name:	Slope intuition
Math Missions:	8th grade (U.S.) Math Mission, Algebra basics Math Mission, Algebra I Math Mission, High school geometry Math Mission
Types of Problems:	2

The Slope intuition exercise appears under the 8th grade (U.S.) Math Mission, Algebra basics Math Mission, Algebra I Math Mission and High school geometry Math Mission. This exercise cultivates the intuition of slope and how lines behave.

Types of Problems

There are two types of problems in this exercise:

1. Graph a line with a certain slope: This problem provides a coordinate grid on which a line can be constructed. Users are expected to graph a line with a given slope.

   

   Graph a line with a certain slope

2. Adjust coefficients to make the line: This problem has a coordinate plane with two blue points. Users are is expected to adjust the slope and y-intercept using the manipulative to create the equation of the line.

   

   Adjust coefficients to make the line

Strategies

Knowledge of lines such as slope and uses of slope-intercept form can help to perform this exercise well.

1. The slope formula is ${\frac{y_2-y_1}{x_2-x_1}}$.
2. It is not necessary to get fancy. It is possible to make a line positive or negative sloped by only moving one point and only moving it slightly. This is the first problem where research has found instances where pressing "Enter" can submit a correct answer with no work.
3. On the Adjust coefficients to make the line problem it is recommended to change slope first by eyeballing, and then moving the y-intercept.

Real-life applications

1. Linear equations show up often in business and many of the sciences.
2. Knowledge of algebra is essential for higher math levels like trigonometry and calculus. Algebra also has countless applications in the real world.