Write a slope intercept equation for a line passing through the point (5,-3) that is parallel to the line 5x+7y=8. then write a second equation for a line passing through the point (5,-3) that is perpendicular to the line 5x+7y=8. so

We're starting with the line

All the lines parallel to it will be of the form

and when our intersection point is (5,-3) the constant must be

That's the answer but we have to turn this into slope intercept form so we solve for y:

y = (-5/7)x + 4/7

For perpendicular lines, we swap the coefficients on x and y, negating one:

Again the point gives the constant:

Solve for y for slope/intercept:

[tex]y = \frac 7 5  x - 10

y = (7/5) x - 10

Let's check with a nice plot:

an

y = 6x -3y -12

y +3y +12 = 6x

=> . x = { 2y / 3 +2 } this is equation of line in terms of x

=> . if line meets the x-axis the co-ordinates of meeting point would be ( x , 0 )

=> . x = 2 ( 0 ) / 3 + 2

=> . x = 2

so, the point is ( 2 , 0 )