Education Technology

Expressions and Equations / Prop. Relationships to Linear Equations

Grade Level 8
Activity 14 of 18
In this lesson students use previous experience with proportional relationships of the form \(y = kx\) to consider relationships of the form \(y = mx\) and eventually \(y = mx+b\).

Planning and Resources

Students should be able to connect the unit rate in a proportional relationship to the slope of its graph using similar triangles, and connect the equation for a proportional relationship, \(y = mx\), to the equation for a line, \(y = mx+b\).

proportional relationship
linear equation

Standard: Search Standards Alignment


Content Group - Lorem


This lesson helps students to use the point slope form of a line to move from graphs of proportional relationships to graph of any line.

What to look for

Student discussion may provide an opportunity to discuss why the denominator of a fraction cannot be zero.

Sample Assessment

Consider the graph of a line.

Which equation has a slope greater than the slope for the line shown?

a. \(y = 3x-1\)      b. \(y = \frac{x}{2}+4\)

c. \(y = 2x+2\)      d. \(y = \frac{x}{3}-3\)

Answer: a

The Big Idea

Any sequence of multiplications may be calculated in any order and the numbers may be grouped together any way.

What are students doing?

They explore different sets of factors that produce the same result and consider whether an exponent can “distribute” over any operation.

What is teacher doing?

Encourage students to explore equivalent ways of writing numerical expressions involving exponents.