Math Snap

STEP 1

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

STEP 2

1. Find the y-intercept.
2. Find the slope.
3. Plot the y-intercept.
4. Use the slope to find another point.
5. Draw the line.

STEP 3

The y-intercept is the value of $y$ when $x = 0$.
Let's substitute $x = 0$ into our equation:
$$y = \frac{2}{5} \cdot 0 + 1$$

STEP 4

Any number multiplied by zero is zero, so $\frac{2}{5} \cdot 0 = 0$.
$$y = 0 + 1$$

STEP 5

Adding zero to a number doesn't change the number, so $0 + 1 = 1$.
$$y = 1$$

STEP 6

So, our y-intercept is $1$, which means the line crosses the y-axis at the point $(0, 1)$.

STEP 7

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

STEP 8

In our equation, $y = \frac{2}{5}x + 1$, the slope $m$ is $\frac{2}{5}$.
This tells us that for every 5 units we move to the right along the x-axis, we move 2 units up along the y-axis.

STEP 9

We found that the y-intercept is $(0, 1)$.
So, let's put a point at $(0, 1)$ on our graph!

STEP 10

Starting from our y-intercept $(0, 1)$, we can use the slope $\frac{2}{5}$ to find another point.

STEP 11

The slope tells us to move 5 units to the right ($+5$ to the $x$-value) and 2 units up ($+2$ to the $y$-value).

STEP 12

Starting at $(0, 1)$, adding $5$ to $x$ gives us $0 + 5 = 5$, and adding $2$ to $y$ gives us $1 + 2 = 3$.

STEP 13

So, our second point is $(5, 3)$.
Let's plot this point on the graph!

STEP 14

Now that we have two points, $(0, 1)$ and $(5, 3)$, we can draw a straight line through them.
Extend the line in both directions to show that it continues infinitely.

The graph of the line $y = \frac{2}{5}x + 1$ is a straight line passing through the points $(0, 1)$ and $(5, 3)$.