Question 626097: write an equation in standard form for the line described.
Through (2,9), perpendicular to 5x + y =2
The equation line is x - ? y = ?.
Answer by NewtonMathCenter(2)   (Show Source):
You can put this solution on YOUR website! First of all, if two lines are perpendicular, then their slopes are opposite reciprocals, or in other words, m and -1/m. Thus, to find the slope of the line given, solve for y so it is in the slope-intercept form.
5x+y=2
-5x -5x
y=-5x+2
The slope-intercept form of the line is y=mx+b where m=slope and b=y-intercept.
So the slope of this line is -5. The slope of a perpendicular line would then be 1/5.
For our new line, so far we have the slope, so if we put it into the slope-intercept form, we have y=1/5x+b. If we then substitute (2,9) for (x,y), we will have 9=1/5(2)+b. Now solve for b:
9=2/5+b
-2/5 -2/5
b=9-2/5
b=45/5-2/5
b=43/5
So we have the equation in slope intercept form now: y=1/5x+43/5. To convert this equation to standard form, move the x and eliminate the fractions by multiplying both sides by the lowest common denominator, 5.
y=1/5x+43/5
-1/5x -1/5x
(-1/5x+y=43/5) 5
-x+5y=43 Standard form should not have a negative coefficient for the x term, so multiply both sides by -1.
x-5y=-43
Excellent work:)
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