Question

Two linear equations are shown below.

y=3x−4


and

x

0

1

2

3

4

y

12

9

6

3

0

How do the slopes for each equation compare?

(2 points)
The slope for y=3x−4
is
, and the slope for the table is
.

Answer 1

To compare the slopes of the equations, we first identify the slope from the equation \( y = 3x - 4 \).

1. **Slope from the equation \( y = 3x - 4 \)**:
The slope (m) from this equation is the coefficient of \( x \), which is **3**.

2. **Slope from the table**:
We can calculate the slope from the values in the table. The slope (m) is calculated using the formula:

\[
m = \frac{\Delta y}{\Delta x}
\]

We can take any two points from the table; let's use the points (0, 12) and (4, 0).

\[
\Delta y = y_2 - y_1 = 0 - 12 = -12
\]
\[
\Delta x = x_2 - x_1 = 4 - 0 = 4
\]

Now, substituting these values into the slope formula:

\[
m = \frac{-12}{4} = -3
\]

So, the slope for \( y = 3x - 4 \) is **3**, and the slope derived from the table is **-3**.

### Summary
- The slope for \( y = 3x - 4 \) is **3**, and the slope for the table is **-3**.