Question

Two linear equations are shown below.

y=3x−4
𝑦
=
3
𝑥
−
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
𝑦
=
3
𝑥
−
4
is , and the slope for the table is .

Answer 1

To determine the slopes of the two equations, we can analyze each one.

1. For the equation \( y = 3x - 4 \):
- The slope is the coefficient of \( x \), which is 3.

2. For the table of values:

The given values are:
- When \( x = 0 \), \( y = 12 \)
- When \( x = 1 \), \( y = 9 \)
- When \( x = 2 \), \( y = 6 \)
- When \( x = 3 \), \( y = 3 \)
- When \( x = 4 \), \( y = 0 \)

To find the slope from these values, we can use the formula for slope \( m \), which is:
\[
m = \frac{\Delta y}{\Delta x}
\]
Taking two points, for example, \( (0, 12) \) and \( (4, 0) \):
- \( \Delta y = 0 - 12 = -12 \)
- \( \Delta x = 4 - 0 = 4 \)

Now we can calculate the slope:
\[
m = \frac{-12}{4} = -3
\]

So, we can summarize:

- The slope for \( y = 3x - 4 \) is **3**.
- The slope from the table is **-3**.

Thus, the complete statement would be:

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