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 three-fourths.
The y-intercept is 2.
The y-intercept is 0.

Answer 1

To determine the equation of the line represented by the points in the table, we first identify the points:

- Point 1: \( (-8, 6) \)
- Point 2: \( (4, -3) \)
- Point 3: \( (8, -6) \)

### Step 1: Calculate the slope (m)

The formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

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

We can use the first two points \((-8, 6)\) and \( (4, -3)\):

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

Let's check the slope with the second and third points \( (4, -3) \) and \( (8, -6) \):

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

Both calculations give the same slope: \( -\frac{3}{4} \).

### Step 2: Find the y-intercept (b)

We can use the slope-intercept form of the equation, which is \(y = mx + b\). Using the slope \(m = -\frac{3}{4}\) and one of the points, let’s use point \( (4, -3) \):

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

Calculating this gives:

\[
-3 = -3 + b
\]
\[
b = 0
\]

Thus, the y-intercept is \(0\).

### Step 3: Write the equation of the line

Using the slope-intercept form:

\[
y = -\frac{3}{4}x + 0 \quad \text{or simply} \quad y = -\frac{3}{4}x
\]

### Conclusion

From this analysis, we can draw the following conclusions:

- Using either slope-intercept or point-slope forms will result in the same equation.
- The slope is Negative three-fourths.
- The y-intercept is 0.

Thus, the correct conclusions from the provided options are:

- **Using either slope-intercept or point-slope forms will result in the same equation.**
- **The slope is Negative three-fourths.**
- **The y-intercept is 0.**