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:
- Point 1: \((-8, 6)\)
- Point 2: \( (4, -3) \)
- 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:
- Using either slope-intercept or point-slope forms will result in different equations. (False)
- Using either slope-intercept or point-slope forms will result in the same equation. (True)
- The slope is Negative four-thirds. (False, the slope is -3/4)
- The slope is Negative four-thirds. (False, the slope is -3/4)
- The y-intercept is 2. (False, the y-intercept is 0)
- 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.