Standard form Ax + By = C
so
<span>(y - y1) = m(x - x1)
</span>given (5, -7) and m = -1/5
so
y + 7 = -1/5(x - 5)
-5y - 35 = x - 5
x + 5y = -30
answer
d. x + 5y = -30
A reflection over the line y=x implies exchanging the x and y coordinates of a point. For example if you take a generic point (a,b) then its reflection over y=x is (b,a). Our point is (-1,3) so its reflection over y=x is the point (3,-1).
Then we have to translate it two units left. Translating a point left means that we are moving towards negative x values so we need to substract 2 from the x coordinate:

Finally we have to translate it 1 unit up towards positive y values so we have to add 1 to its y coordinate:

And these are the final coordinates. In the following picture you have the points you get after each step (from A to D) with the y=x line in blue:
he equation of a line is written as y=mx+b where m is the slope and b is the
y -intercept, Thus,m=23 And the y -intercept,b=1