# LINR 1 | Lesson 1 | Making Connections (Equations)

## Equations

How can you use the pattern’s equation to find the slope and the $$y$$-intercept?

• The equation shows both the slope (growth rate) and the $$y$$-intercept which is the number of squares in Step $$0$$.

Use Pattern 1 below to determine the slope and $$y$$-intercept.

• Pattern 1 grows by 2 squares $$s(n)$$ for every one step $$n$$.
• Pattern 1 has 4 squares at Step 0, which is the starting point or the $$y$$-intercept of $$(0,4)$$.
• The equation for Pattern 1 is: $$s(n)=2n+4$$, where $$n$$ represents the step number and $$s(n)$$ represents the number of squares at any given step $$n$$.
• The slope of 2 is the coefficient of $$n$$ and the $$y$$-intercept $$(0,4)$$ is the constant. This equation gives the rule to start with 4 at Step $$0$$ and add 2 for each step.
1. Circle the slope and underline the $$y$$-intercept for the remaining pattern equations.

Pattern 2 Equation: $$s(n)=2n+1$$

Pattern 3 Equation: $$s(n)=3n+2$$

Pattern 4 Equation: $$s(n)=3n+1$$ 