To find the equation of the line that passes through the points \((-1, -9)\) and \( (1, 7) \), we first need to calculate the slope \(m\) of the line using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the coordinates:
- \((x_1, y_1) = (-1, -9)\)
- \((x_2, y_2) = (1, 7)\)
Substituting the values into the slope formula:
\[ m = \frac{7 - (-9)}{1 - (-1)} = \frac{7 + 9}{1 + 1} = \frac{16}{2} = 8 \]
Now that we have the slope \(m = 8\), we can use the point-slope form of the line to write the equation. Let's use the point \((-1, -9)\):
The point-slope form is given by:
\[ y - y_1 = m(x - x_1) \]
Substituting \(m = 8\), \(x_1 = -1\), and \(y_1 = -9\):
\[ y - (-9) = 8(x - (-1)) \] \[ y + 9 = 8(x + 1) \] \[ y + 9 = 8x + 8 \]
Next, we solve for \(y\):
\[ y = 8x + 8 - 9 \] \[ y = 8x - 1 \]
Thus, the equation of the line in slope-intercept form is:
\[ \boxed{y = 8x - 1} \]
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