Which is the equation in slope-intercept form for the line that passes through (2, 8) and is perpendicular to 4x + 2y = 6?

Question

imstuck · Answer

Ok, the rule about lines being perpendicular to one another is that their slopes are opposite reciprocals of one another.  This means that if one line has a slope of 2, the line that runs perpendicular to it will have a slope of -1/2.  Does that sound familiar?

jdoe0001 · Answer

what's the slope of -> 4x + 2y = 6?

imstuck · Answer

Ok, first let's find the slope of the equation.  Remember you will solve for y here.  Get y alone.  2y = -4x + 6.  Solve for y:  y = -4/2x + 6.  The -4/2 will reduce to -2.  So the slope of that line is -2. The opposite reciprocal of - 2 is a positive 1/2 (the reciprocal of 2 is 1 over 2).  Now that we have a slope value (which is denoted as "m", don't ask me why), we can use the point we have in a point-slope formula to find the equation.

rissyroo118 · Answer

a y=-1/2x+7
b y=1/2x+7
c y= -2x+12
d y=2x+4

imstuck · Answer

The point-slope formula looks like this$$y - y _{1}=m(x-x _{1})$$where the y1 and the x1 are coordinates from your given point of (2, 8).  2 is the x coordinate and 8 is the y coordinate.  $$y - 8 = \frac{ 1 }{ 2 }(x-2)$$Now wed distribute the 1/2 into the paranthesis to get$$y-8=\frac{ 1 }{ 2 }x-\frac{ 2 }{ 2 }$$which is actually $$y-8=\frac{ 1 }{ 2 }x-1$$Now add the 8 that is with the y to both sides to get $$y=\frac{ 1 }{ 2 }x+7$$That's  your equation that is perpendicular to the one they gave you

rissyroo118 · Answer

now - 
Which is the equation of a line perpendicular to the line with the equation 3x + 4y = 7?
       4x + 3y = 3
       4x – 3y = 5
       3x – 4y = 3
       3x + 4y = 5

rissyroo118 · Answer

@IMStuck

imstuck · Answer

I'm back now!

rissyroo118 · Answer

i figured that one out. its b (:

imstuck · Answer

First solve it for y.  Move the 3x over to the other side using subtraction.  4y = -3x + 7.  Now you have to divide everything by 4 to get the y all alone (y's appear to be very lonely, don't they?).  When you do that you get y = -3/4x + 7/4.  The slope here is -3/4.  The opposite reciprocal is 4/3 (positive).  Now let's test our choices for the one that gives us a slope of 4/3.

imstuck · Answer

Oh, you're right! It is B!!! Good!