Question 427073
Solution:First we find the slope of 7x-10y=18 => -10y=18-7x => {{{y=(7/10)*x-(18/10)}}}

From the last equation we see the slope is {{{m[1]=7/10}}}. As we know the perpendicular lines have negative reciprocal slopes, thus the slope of our line is {{{m[2]=-10/7}}}, and the equation of our line that passes at (14,-2) is given:

{{{y+2=(-10/7)*(x-14)}}}, simplify this equation:

  7y+14=-10x+140 => 7y=-10x+126 => {{{y=(-10/7)x+126}}}

 Answer: The slope-intercept equation is: {{{y=(-10/7)*x+126}}}