# 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

Objective
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, $$y = mx+b$$.

Vocabulary
proportional relationship
linear equation
intercept

Standard:

## Content Group - Lorem

#### Understanding

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.