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.