Question

What is the equation of the line with points represented in the table?

A 2-column table with 3 rows. Column 1 is labeled x with entries negative 8, 4, 8. Column 2 is labeled y withentries 6, negative 3, negative 6.

What can you conclude about the line represented in the table? Select all that apply.

Using either slope-intercept or point-slope forms will result in different equations.
Using either slope-intercept or point-slope forms will result in the same equation.
The slope is Negative four-thirds.
The slope is Negative four-thirds.
The y-intercept is 2.
The y-intercept is 0.

Answer 1

To find the equation of the line represented by the points in the given table, we'll first calculate the slope (m) using the formula:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Using the points from the table:
1. Point 1: \((-8, 6)\)
2. Point 2: \( (4, -3) \)
3. Point 3: \( (8, -6) \)

Let's choose two points, say \((-8, 6)\) and \( (4, -3) \):

\[
m = \frac{-3 - 6}{4 - (-8)} = \frac{-9}{4 + 8} = \frac{-9}{12} = -\frac{3}{4}
\]

Now let's also check another pair of points, say \( (4, -3) \) and \( (8, -6) \):

\[
m = \frac{-6 - (-3)}{8 - 4} = \frac{-6 + 3}{4} = \frac{-3}{4}
\]

Thus, the slope \( m \) of the line connecting these points is consistent, and it is indeed \(-\frac{3}{4}\).

Now, let’s find the y-intercept (b) using the slope-intercept form equation \( y = mx + b \) with one of the points, say \( (4, -3) \):

\[
-3 = -\frac{3}{4}(4) + b
\]
\[
-3 = -3 + b \Rightarrow b = 0
\]

So the equation of the line is:

\[
y = -\frac{3}{4}x
\]

Now, let's review the statements provided in the question:

1. Using either slope-intercept or point-slope forms will result in different equations. **(False)**
2. Using either slope-intercept or point-slope forms will result in the same equation. **(True)**
3. The slope is Negative four-thirds. **(False, the slope is -3/4)**
4. The slope is Negative four-thirds. **(False, the slope is -3/4)**
5. The y-intercept is 2. **(False, the y-intercept is 0)**
6. The y-intercept is 0. **(True)**

### Conclusion:
- The correct statements are:
- Using either slope-intercept or point-slope forms will result in the same equation.
- The y-intercept is 0.