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 $$(-2, -1)$$.

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

\begin{align}y-2&=\dfrac{3}{2}(x-0)\\\\ y-2&=\frac{3}{2}x\\\\ y&=\dfrac{3}{2}x+2\end{align}

1. 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) $$3$$ $$2\dfrac{3}{8}$$ $$6$$ $$2\dfrac{3}{4}$$ $$9$$ $$3\dfrac{1}{8}$$ $$12$$ $$3\dfrac{1}{2}$$
1. 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 $$2\dfrac{3}{8}$$ and $$2\dfrac{3}{4}$$ is $$\dfrac{3}{8}$$.
• The change between $$2\dfrac{3}{4}$$ and $$3\dfrac{1}{8}$$ is $$\dfrac{3}{8}$$.
• The change between $$3\dfrac{1}{8}$$ and $$3\dfrac{1}{2}$$ is $$\dfrac{3}{8}$$.

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

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

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

Equation:  $$y = \dfrac{1}{8}x+2$$

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

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