Math Snap

STEP 1

What is this asking?
Draw the line represented by the equation $y = -\frac{2}{5}x + 1$ on the coordinate plane.
Watch out!
Don't mix up the slope and the y-intercept!

STEP 2

1. Identify the y-intercept.
2. Identify the slope.
3. Plot the y-intercept.
4. Use the slope to find a second point.
5. Draw the line.

STEP 3

The equation is in slope-intercept form, which is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

STEP 4

In our equation, $y = -\frac{2}{5}x + 1$, the y-intercept is $b = \mathbf{1}$.
This tells us that the line crosses the y-axis at the point $(0, 1)$.

STEP 5

In our equation, $y = -\frac{2}{5}x + 1$, the slope is $m = \mathbf{-\frac{2}{5}}$.

STEP 6

Remember, the slope is the "rise over run".
A negative slope means the line goes down as we move from left to right.

STEP 7

We found that the y-intercept is $\mathbf{1}$, so we plot the point $(0, 1)$ on the graph.
This is our starting point.

STEP 8

Our slope is $-\frac{2}{5}$.
This means for every 5 units we move to the right along the x-axis (the run), we move 2 units down along the y-axis (the rise).

STEP 9

Starting from our y-intercept $(0, 1)$, we move 5 units to the right, which takes us to $x = 5$.

STEP 10

Then, we move 2 units down from $y = 1$, which takes us to $y = 1 - 2 = -1$.

STEP 11

So, our second point is $(5, -1)$.

STEP 12

Now that we have two points, $(0, 1)$ and $(5, -1)$, we can draw a straight line through them.
Make sure your line extends to the edges of the graph!

The line passing through the points $(0, 1)$ and $(5, -1)$ represents the graph of the equation $y = -\frac{2}{5}x + 1$.