To find the slope of the line that passes through the points \((-9, 41)\) and \( (2, -3)\), you can use the slope formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Here, \((x_1, y_1) = (-9, 41)\) and \((x_2, y_2) = (2, -3)\).
Plugging in these values:
\[ m = \frac{-3 - 41}{2 - (-9)} = \frac{-3 - 41}{2 + 9} = \frac{-44}{11} = -4 \]
So, the slope \(m\) is \(-4\).
Next, we can find the vertical intercept (y-intercept). The vertical intercept occurs where \(x = 0\). We can use the point-slope form of a line:
\[ y - y_1 = m(x - x_1) \]
Using one of the points, let’s use \((-9, 41)\):
\[ y - 41 = -4(x + 9) \]
Expanding this gives:
\[ y - 41 = -4x - 36 \]
Adding 41 to both sides:
\[ y = -4x + 5 \]
Thus, the vertical intercept is \(5\).
Now we can summarize:
- Slope: \(-4\)
- Vertical Intercept: \(5\)
- Equation of the Line: \(y = -4x + 5\)
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