what equation is perpendicular to 2x+5y=13 and goes through (7,-1)

Question

It needs to be perpendicular and go through the point (7,-1)

Answer 1

Now, once and never again, change the Standard Form of the equation of a line (Ax + By = C) into slope-intercept form (y=mx + b) and remember that:

  (1)  the slope of the line is -A/B

  (2)  the slope of all perpendicular lines is B/A

  (3)  the equation of all perpendicular lines is:  Bx - Ay = D     (with D≠C)

  (4)  the y-intercept is C/B

  (5)  the x-intercept is C/A

Note:  the Standard Form of an equation of a line can also be used to express vertical lines !!

 

The problem gives:

     2x + 5y = 13

The equation of all perpendicular lines is:

     5x - 2y = D        [ so we need to point (7,-1) to compute D ]

     5(7) -2(-1) = D

      37 = D

      5x - 2y = 37    (give answer in Standard Form since problem used it)

Answer 2

This problem involves different parts: determining the slope of the first equation, the slope of the line perpendicular to it, and the exact equation of the perpendicular line going through the point (7,-1).

 

First, let's determine the slope of the first equation. To do this, we need to put it in slope intercept form so it explicitly states the slope. We need to rearrange the equation so y is isolated (slope intercept form is y=mx+b with m as the slope and b as the y intercept). The 2x must be moved to the other side of the equation through subtracting it from both sides like so: 2x-2x+5y=13-2x or 5y= -2x+13. Isolating the y, you divide both sides by 5 resulting in the equation y= (-2/5)x +(13/5). Since the slope is the value in front of the x, the slope is -2/5.

 

Now that the slope is found, we need the slope for the line that would be perpendicular to it. For linear equations, the perpendicular slope must be going in the opposite direction in a way that forms as 90° angle. So the perpendicular slope is the opposite reciprocal of the original slope making the perpendicular slope 5/2.

 

The problem asks for the exact equation of the perpendicular slope that would go through (7, -1). As an equation, the perpendicular equation would be: y= 5/2x +b since the y intercept is unknown. You would then use the given point to help you– (7, -1) is for x, y respectfully so substitute those values into the equation! Doing so gives you this: -1= (5/2)•7 +b. Now solve for b and you will have the answer!

 

 

 

Answer 3

The equation can be rewritten as, 5y= -2x +13 or, y= -(2/5)x + 13/5

Therefore the slope for this is -2/5. The slope of the line perpendicular to this line is 5/2.

The general equation of this line is, y= 5/2 x + c

Since the line passes through (7,-1) we can plug-in the equation,

Thus,  -1=5/2 x 7+c

Therefore c= -1-35/2 = - 37/2

Thus the equation is, y= 5/2 x - 37/2

or, 2y = 5x -37

0r, 5x-2y=37