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?

dude just pls help me

Answer 1

Let's analyze the given information step by step.

1. **Equation Provided**: The equation given is:
\[
y = 3x - 4
\]
- In this equation, the coefficient of \(x\) (which is 3) represents the slope of the line.
- Therefore, the slope of this linear equation is \(3\).

2. **Table Data**: You provided the following data points:
```
x: 0 1 2 3 4
y: 12 9 6 3 0
```
We can determine the slope of the line represented by this table of values by calculating it between any two points.

Using the points \((0, 12)\) and \((4, 0)\):
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 12}{4 - 0} = \frac{-12}{4} = -3
\]

3. **Comparing the Slopes**:
- The slope of the first equation \(y = 3x - 4\) is \(3\).
- The slope calculated from the table values is \(-3\).

To summarize:
- The slope of \(y = 3x - 4\) is \(3\).
- The slope derived from the table data is \(-3\).

**Comparison**: The slopes are different; specifically, one is positive (3) and the other is negative (-3).