Math Snap

STEP 1

What is this asking?
We need to find the $y$ values for some given $x$ values in a linear equation and then graph the line.
Watch out!
Don't mix up your $x$ and $y$ values!
Also, make sure your graph matches the table.

STEP 2

1. Substitute and Solve
2. Graph It

STEP 3

Alright, let's kick things off with $x = -5$!
We've got our equation: $y = -\frac{x}{5} + 2$.
Let's plug in our $x$ value: $y = -\frac{-5}{5} + 2$.

STEP 4

A negative divided by a negative is a positive, so $-\frac{-5}{5}$ becomes $\frac{5}{5}$, which simplifies to 1.
So, $y = 1 + 2 = \textbf{3}$.
When $x = -5$, $y = \textbf{3}$!

STEP 5

Next up, $x = 0$!
Substituting into our equation: $y = -\frac{0}{5} + 2$.

STEP 6

Zero divided by anything is just zero, so we have $y = 0 + 2 = \textbf{2}$.
When $x = 0$, $y = \textbf{2}$!

STEP 7

Last one for the table: $x = 5$!
Plugging it in: $y = -\frac{5}{5} + 2$.

STEP 8

$-\frac{5}{5}$ simplifies to $-1$, giving us $y = -1 + 2 = \textbf{1}$.
So when $x = 5$, $y = \textbf{1}$!

STEP 9

Now for the fun part!
We've got our points: $(-5, 3)$, $(0, 2)$, and $(5, 1)$.
Let's plot these bad boys on a graph.

STEP 10

Remember, the first number in each pair is our $x$ value (how far we go left or right), and the second number is our $y$ value (how far we go up or down).

STEP 11

Once you've plotted the three points, grab your ruler (or any straight edge) and draw a line right through them!
Extend the line beyond the points in both directions, because the equation represents an infinite line, not just the three points we calculated.

Our completed table:
$$\begin{array}{cc} x & y \\ -5 & 3 \\ 0 & 2 \\ 5 & 1 \\ \end{array}$$And we've got our graph with the line passing through $(-5, 3)$, $(0, 2)$, and $(5, 1)$!