Math Snap

STEP 1

What is this asking?
How does the number of pregnancies change when years of schooling goes up by one?
Watch out!
Don't mix up the slope and the y-intercept!
We're looking at changes, so focus on the slope.

STEP 2

1. Understand the Equation
2. Interpret the Slope

STEP 3

Alright, so we've got this cool equation, $\hat{y} = 4 - 3x$.
This tells us how the number of pregnancies ($\hat{y}$) changes based on the years of schooling ($x$).
It's a linear equation, which means it's a straight line!

STEP 4

Remember, a linear equation is in the form $\hat{y} = mx + b$.
Here, $m$ is the slope (how steep the line is) and $b$ is the y-intercept (where the line crosses the y-axis).

STEP 5

Let's match our equation, $\hat{y} = 4 - 3x$, to the general form.
Notice, we can rewrite our equation as $\hat{y} = -3x + 4$.
Now, it's super clear that our slope is $m = -3$ and our y-intercept is $b = 4$.

STEP 6

The slope tells us how much $\hat{y}$ (number of pregnancies) changes when $x$ (years of schooling) increases by one.
In our case, the slope is $-3$.

STEP 7

A negative slope means that as $x$ increases, $\hat{y}$ decreases.
So, as years of schooling increase, the number of pregnancies decreases.

STEP 8

Specifically, our slope is $-3$.
This means that for every one year increase in schooling, the number of pregnancies tends to decrease by 3.
Boom!

The correct interpretation is: When the amount of schooling increases by one year, the number of pregnancies tends to decrease by 3.