To find the equation of a line in slope-intercept form \( y = mx + b \), we start with the slope \( m \) and a point that the line passes through.
Given:
- Slope \( m = -7 \)
- Point \( (2, 7) \)
We can substitute the slope and the coordinates of the point into the equation and solve for \( b \) (the y-intercept).
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Use the slope-intercept form: \[ y = mx + b \] Substitute \( m = -7 \) and the point \( (x, y) = (2, 7) \): \[ 7 = -7(2) + b \]
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Calculate \( -7(2) \): \[ 7 = -14 + b \]
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Add 14 to both sides to solve for \( b \): \[ 7 + 14 = b \quad \Rightarrow \quad b = 21 \]
Now we have both \( m \) and \( b \):
- Slope \( m = -7 \)
- Y-intercept \( b = 21 \)
Thus, the equation in slope-intercept form is: \[ y = -7x + 21 \]
So, the final answer is: \[ \boxed{y = -7x + 21} \]