Find the equation in slope/intercept form that is perpendicular to 2x - 3y = 4 and passing through (-1/7, 4).

y = -1½x + 3 11⁄14

Step-by-step explanation:

First convert from Standard Form to Slope-Intercept Form:

2x - 3y = 4

-2x- 2x

-3y = -2x + 4

___

-3-3

y = ⅔x - 1⅓ >> Slope-Intercept Form

↑

slope

Now, Perpendicular Lines have OPPOSITE MULTIPLICATIVE INVERSE Rate of Changes [Slopes], so since the slope is ⅔, the opposite multiplicative inverse of that would be -1½, or -3⁄2. Anyway, do the following:

4 = -1½[-⅐] + b

3⁄14

-3⁄14 - 3⁄14

3 11⁄14 = b

y = -1½x + 3 11⁄14 >> New equation

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Step-by-step explanation:

So a few things to know before hand.  Slope ntercept form is y = mx + b where m is the slope, and in this form that will always make b the y intercept.

A perpendicular slope is pretty easy to find.  Of course, perpendicular means it intersects that first line at a 90 degree angle.  So the x and y axis themselves are perpendicular.  Anyway, if you know the slope of the line, a perpendicular slope is -1/m where m is the slope.  S taking the simplest example, in the graph of just x, the slope is 1, so the perpendicular slope is -1/1 or just -1.

The last thing is to know how to write the equation of a linear function when you know a point and its slope.  if you have the slope m and a point on the graph (a,c) you can use the point slope form which is this.  y - c = m(x - a) where you solve for y.  x an y stay as variables here.

Now knowing all that we can start.  First we want to put the original graph into slope intercept form, which is pretty easy.  Just manipulate the equation.

2x - 3y = 4

2x -4 = 3y

y = (2x - 4)/3

y = 2/3 x - 4/3

so m = 2/3 and b = -4/3

Now, we have the slope of this line and want the slope of a perpendicular line.  Like I mentioned before the slope is -1/m so in this case that's -1/(2/3) = -3/2  Let me know if you don't get how that was gotten.

Now that we kno the perpendicular slope, we can make a perpendicular line.  How do we make a line when we know the slope and a point?  Keep in mind the point is (-1/7, 4)

y - c = m(x-a)

y - 4 = -3/2(x + 1/7)

y - 4 = -3/2 x - 3/14

y = -3/2 x + 53/14

If it weren't in slope intercept form you'd have to put it in that, but I took care of it in the process, so here's the answer.  Let me know if there's anything you don't understand.  

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