May Ray
07/07/2023 · High School
Write the equation of the line, with the given properties, in slope-intercept form, Slope \( =-2 \), through \( (-5,9) \) The equation of the line is
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To find the equation of the line in slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept, we can use the point-slope form of the equation of a line.
Given:
- Slope \( m = -2 \)
- Point on the line \( (-5, 9) \)
The point-slope form of the equation of a line is:
\[ y - y_1 = m(x - x_1) \]
Substitute the values of the slope and the point into the point-slope form:
\[ y - 9 = -2(x - (-5)) \]
\[ y - 9 = -2(x + 5) \]
\[ y - 9 = -2x - 10 \]
\[ y = -2x - 10 + 9 \]
\[ y = -2x - 1 \]
Therefore, the equation of the line in slope-intercept form is \( y = -2x - 1 \).
Quick Answer
The equation of the line is \( y = -2x - 1 \).
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