To find the slope \( m \) of the line that passes through the points \((-3, 8)\) and \((4, -6)\), we will use the slope formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Assigning the coordinates:
- \( (x_1, y_1) = (-3, 8) \)
- \( (x_2, y_2) = (4, -6) \)
Now, substituting the values into the formula:
\[ m = \frac{-6 - 8}{4 - (-3)} = \frac{-6 - 8}{4 + 3} = \frac{-14}{7} = -2 \]
So, the slope \( m \) is:
\[ m = -2 \]
Next, we will use the slope-intercept form \( y = mx + b \) to find the y-intercept \( b \). We can use one of the given points and the slope. Let's use the point \((4, -6)\) with the slope \( m = -2 \):
Using the point-slope formula:
\[ y = mx + b \] \[ -6 = -2(4) + b \]
Calculating the right side:
\[ -6 = -8 + b \]
To isolate \( b \):
\[ b = -6 + 8 = 2 \]
Now we have the y-intercept \( b \):
\[ b = 2 \]
Finally, we can write the equation in slope-intercept form:
\[ y = mx + b \] \[ y = -2x + 2 \]
So, the final equations are:
- Slope \( m = -2 \)
- Y-intercept \( b = 2 \)
- Equation in slope-intercept form: \( y = -2x + 2 \)
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