Question The point (-6, 4) lies on a straight line that has a gradient of -2. What is the equation of this line?
Given: Point on straight line = (-6,4) Gradient = -2 To find: The equation of the line. Solution: Point-slope form: If a line passes through the point [tex](x_1,y_1)[/tex] with slope m, then the equation of the line is [tex]y-y_1=m(x-x_1)[/tex] The line passes through the point (-6,4) with slope -2. So, the equation of the line is: [tex]y-4=-2(x-(-6))[/tex] [tex]y-4=-2(x+6)[/tex] [tex]y-4=-2x-12[/tex] Adding 4 on both sides, we get [tex]y-4+4=-2x-12+4[/tex] [tex]y=-2x-8[/tex] Therefore, the equation of the line is [tex]y=-2x-8[/tex]. Log in to Reply
Given:
Point on straight line = (-6,4)
Gradient = -2
To find:
The equation of the line.
Solution:
Point-slope form: If a line passes through the point [tex](x_1,y_1)[/tex] with slope m, then the equation of the line is
[tex]y-y_1=m(x-x_1)[/tex]
The line passes through the point (-6,4) with slope -2. So, the equation of the line is:
[tex]y-4=-2(x-(-6))[/tex]
[tex]y-4=-2(x+6)[/tex]
[tex]y-4=-2x-12[/tex]
Adding 4 on both sides, we get
[tex]y-4+4=-2x-12+4[/tex]
[tex]y=-2x-8[/tex]
Therefore, the equation of the line is [tex]y=-2x-8[/tex].