write an equation that satisifies the given conditions: perpendicular to y=-3x+7 through (3,5)

Answer 1

In this case, the slope of the given line is m=-3. The slope of the perpendicular line is m1 such that m.m1=-1.
Therefore m1=-1/(-3)=1/3
If it has to pass through a point (x1,y1), the equation of the line is then
y=m1(x-x1)+y1

Can you continue from here?

Answer 2

The equation for a straight line is y = mx + b where m is the slope. Therefore, the slope of this line is -3. The line perpendicular to this line has a slope of the negative reciprocal or 1/3.
y = (1/3)x + 7 or
3y = x + 21
Now substitute either value for x or y and solve for the other; for example, substitute 5 for y and solve for x, then write it in standard form.