# LINR 1 | Lesson 4 | Try This! (Solution: Write Equations Using Point-Slope)

## Solution: Write Equations Using Point-Slope

1. Use the Point-Slope formula to write the equation of the line between the points $$(0,2)$$ and $$(-2, -1)$$.

$slope=\frac{-1-(2)}{-2-(0)}=\frac{-3}{-2}=\frac{3}{2}$

$y-2=\frac{3}{2}(x-0)$

$y-2=\frac{3}{2}x$

$y=\frac{3}{2}x+2$

2.  To check if a relationship is linear, we would need to see that there is a constant rate of change between any of the values in the table.  We do this by evaluating the change in $$x$$ and the change in $$y$$.

 Number of cups in the stack Height of the stack (inches) $$3$$ $$2\Large\frac{3}{8}$$ $$6$$ $$2\Large\frac{3}{4}$$ $$9$$ $$3\Large\frac{1}{8}$$ $$12$$ $$3\Large\frac{1}{2}$$

a.  Since the domain ($$x$$-values) increase by the constant 3, we next determine if the range ($$y$$-values) also increase or decrease by a constant amount.

• The change between $$2\frac{3}{8}$$ and $$2\frac{3}{4}$$ is $$\frac{3}{8}$$.
• The change between $$2\frac{3}{4}$$ and $$3\frac{1}{8}$$ is $$\frac{3}{8}$$.
• The change between $$3\frac{1}{8}$$ and $$3\frac{1}{2}$$ is $$\frac{3}{8}$$.

Since the $$y$$-values are increasing by $$\frac{3}{8}$$ and the $$x$$-values are increasing by 3, the relationship is linear.

b.  By selecting two points from the table ($$3, 2\frac{3}{8})$$ and ($$9, 3\frac{1}{8})$$, we can calculate the slope as $$\large(\frac{3\frac{1}{8} -2\frac{3}{8}}{9 – 3})$$ = $$\frac{1}{8}$$

Use point slope to find the equation:  $$(y – 2\frac{3}{8}) = \frac{1}{8}(x – 3)$$

Equation:  $$y = \frac{1}{8}x + 2$$

c.  The equation tells us that the height of the stack grows by $$\frac{1}{8}$$ inches for every cup added, and that the height of the shelf is 2 inches.

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