(5,-7); 2x+7y=8

Question

Write an equation for a line passing through ?(5?,−7?) and perpendicular to the line
2x+7y=8.

Answer 1

PLZ, ONCE AND FOREVER, convert the Standard Format of a line (Ax+By=C) to slope-intercept form (y=mx+b) and get y=(-A/B)x+(C/B) and remember:

  -- the slope is (-A/B), so all perpendicular lines have slope (B/A) [the negative reciprocal of (-A/B)]

  -- the y-intercept is (C/B).

 

The slope of line 2x+7y=8 is (-2/7).  The slope of all perpendicular lines is (7/2).

The equation of all perpendicular lines is:

      7x - 2y = D     [and we need a point like (5,-7) to determine D]

      7(5) - 2(-7) = D

      35 +14 = D

        49 = D

The equation of the perpendicular line, in Standard Format, is:   7x - 2y = 49

  Remember how to convert that?   y = -(7/(-2))x + (49/(-2))

                                                          y = (7/2)x - 49/2

Answer 2

Jarius,

 

A line which is perpendicular to another line has a slope which is the negative inverse of the first line.

 

You are given

2x+7y=8

 

Restate this in slope-intercept form to get the slope

2x+7y=8

7y=8-2x

7 = 8/7 - 2/7x

 

The slope is -2/7

And the slope of the perpendicular line is 7/2.

 

Now we need a line with a slope of 7/2 that passes through the point (5,-7).

 

For this we use the point-slope form of an equation of a line.

y-y₁ = m(x-x₁), where (x₁,y₁) is the point and m is the slope.

y+7 = (7/2)(x-5)

 

Cleaning this up

y + 7 = (7/2)x - (7/2)5

y +7 = (7/2) x - 35/2

y = (7/2)x - 35/2 - 14/2

y = (7/2)x - 49/2

 

If you need the equation in standard form, which is the form given in the question, multiply the both sides by 2

2y = 7x - 49

7x - 2y = 49