Write an equation of the line that passes through the point $(-2,-4)$ with slope -6.
A. $y+4=-6(x+4)$
B. $y+2=-6(x+2)$
C. $y+2=6(x+4)$
D. $y+4=-6(x+2)$
Answer (2)
Use the point-slope form of a line: y − y 1 = m ( x − x 1 ) .
Substitute the given point ( − 2 , − 4 ) and slope -6 into the point-slope form: y − ( − 4 ) = − 6 ( x − ( − 2 )) .
Simplify the equation: y + 4 = − 6 ( x + 2 ) .
The equation of the line is y + 4 = − 6 ( x + 2 ) .
Explanation
Understanding the Problem We are given a point ( − 2 , − 4 ) and a slope m = − 6 . We need to find the equation of the line that passes through this point with the given slope.
Using Point-Slope Form The point-slope form of a linear equation is given by: y − y 1 = m ( x − x 1 ) where ( x 1 , y 1 ) is a point on the line and m is the slope of the line.
Substituting the Values Substitute the given point ( − 2 , − 4 ) and slope m = − 6 into the point-slope form: y − ( − 4 ) = − 6 ( x − ( − 2 ))
Simplifying the Equation Simplify the equation: y + 4 = − 6 ( x + 2 )
Finding the Correct Option Comparing the obtained equation with the given options, we find that option D matches our equation. Therefore, the equation of the line is: y + 4 = − 6 ( x + 2 )
Examples
Imagine you're designing a ramp for a skateboard park. You know the ramp needs to pass through a certain point and have a specific steepness (slope). Using the point-slope form, you can determine the exact equation of the ramp, ensuring it meets the required specifications. This ensures the ramp is safe and fun for skateboarders.
The equation of the line passing through the point ( − 2 , − 4 ) with a slope of − 6 is derived using point-slope form, resulting in y + 4 = − 6 ( x + 2 ) . Thus, the correct answer is option D.
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