Question

Finf the equation of the line through the intersection of lines 3x+4y=7 and x-y+2=0 and whose slope is 5

Answer 1

hope it's correct !!

Answer 2

$\Large{\textbf{\underline{\underline{According\;to\;the\;Question}}}}$

Given,

Lines = 3x + 4y = 7 & x - y + 2 = 0

Equation of any line through the point of intersection of given lines is of form :-

(3x + 4y - 7) + k(x - y + 2) = 0 ... (1)

Taking common,

(3x + k)x + (4 - k)y + 2(k - 7) = 0

(4 - k)y = -(3 + k)x + (7 - 2k)

y = -{(3 + k)/4 - k}x + (7 - 2k)/(4 - k)

y = {(k + 3)/k - 4}x + (7 - 2k)/(4 - 2k)

Slope

= (k + 3)/(k - 4)

Therefore,

k + 4/k - 4 = 5

k + 3 = 5k - 20

4k = 23

k = 23/4

Putting value of k in (1),

(3x + 4y - 7) + 23/4(x - y + 2) = 0

4(3x + 4y - 7) + 23(x - y + 2) = 0

35x - 7y + 18 = 0

Hence,

Required Equation = 35x - 7y + 18 = 0