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Question 37207: Write the equation of the line L satisfying the given geometric conditions.
L has y-intercept (0,2) and is perpendicular to the line with equation 2x-3y=6
I am able to solve this style of equation when the line is parallel and when the y variable is already by itself. I can't seem to figure this one out. Help, please!
Answer by Nate(3500)   (Show Source):
You can put this solution on YOUR website! First, let us determine the slope of the equation:
2x-3y=6
-3y=-2x+6
y=(2/3)x-2
| Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc |
Equation  describes a sloping line. For any
equation ax+by+c = 0, slope is  .- X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 6/2 = 3.
- Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 6/-3 = -2.
- Slope is -2/-3 = 0.666666666666667.
- Equation in slope-intercept form: y=0.666666666666667*x+-2.
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The slope is perpendicular to (2/3), so the slope is the opposite of the recipricol (-3/2).
Write the equation of the line L satisfying the given geometric conditions.
L has y-intercept (0,2).
use: y-(y point)=m(x-(x point))
y-2=(-3/2)x
y=(-3/2)x+2 the equation
| Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc |
Equation  describes a sloping line. For any
equation ax+by+c = 0, slope is  .- X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 2/1.5 = 1.33333333333333.
- Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 2/1 = 2.
- Slope is -1.5/1 = -1.5.
- Equation in slope-intercept form: y=-1.5*x+2.
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