Question 436788
First write the equation of the line in the slope-intercept form:

{{{y=(-4/7)x+(9/7)}}} the slope of this line is m1=-4/7

Second we find the slope of the line perpendicular to the line {{{y=(-4/7)x+9/7}}}

We know perpendicular lines have reciprocal negative slopes: m2=-1/m1, therefore

m2=7/4. Now we write the equation of the line through the point (7, 3) and 

perpendicular to the line {{{y=(-4/7)x+9/7}}}:

{{{y-3=(7/4)(x-7)}}}, write it in standard form: {{{4(y-3)=7(x-7)}}}} =>

{{{7x-4y=37}}}.

Done.