SOLUTION: give the slope-intercept form of the equation of the line that is perpendicular to -6x-4y=6 and contains the point (7,4) and the answer is y=2/3x - 2/3. i just need to know the ste
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Question 248055: give the slope-intercept form of the equation of the line that is perpendicular to -6x-4y=6 and contains the point (7,4) and the answer is y=2/3x - 2/3. i just need to know the steps to get to that answer
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
set the equation up in the format y=mx+b where m=slope and b is the y intercept.
y=2/3x-2/3
4=2/3(7)-2/3
multiply by 3
12=2*7-2
12=14-2
yes that is a line that passes through (7,4)
first we have to find the slope of the original equation.
so we manipulate it to the form y=mx+b
-6x-4y=6
we want the y alone on one side
add 4y to both sides
-6x=6+4y
subtract 6 from both sides
-6x-6=4y
divide both sides by 4
-6/4x-6/4=y
-3/2x-3/2=y
y=-3/2x-3/2
the slope is -3/2 and the y intercept when x=0 is -3/2
ok now we want to find a line with a slope that when multiplied by -3/2 gives us minus 1
-(3/2)*x=-1
divide both sides by -3/2
divide by -3/2 is the same as multiplying by -2/3
-3/2(-2/3)x=-1(-2/3)
x=1(2/3)
x=2/3
so the new line perpendicular has a slope of 2/3
and passes through (7,4)
so now we know everything but the y intercept b
so we plug 7,4 into our new equation
y=mx+b
4=2/3(7)+b
multiply by 3
12=14+3b
subtract 14 from both sides
-2=3b
divide both sides by 3
-2/3=b
now we have all we need for the new equation
y=2/3x-2/3
Was that fun or what!?
I bet you just want to do another dozen just like this.
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