Answer: y = 2x + 1
Step-by-step explanation:
Rewrite the equation in standard form:
x+2y=5
2y = -x + 5
y = -(1/2)x + (5/2)
A line perpendicular to this would have a slope that is the negative inverse of the reference line slope, -(1/2), here. The new slope would be 2. The y-intercept, (5/2), will change, so we'll just use b for the new y-intercept, and calculate it later:
y = 2x +b
We know that point (3,7) lies on the new line (it is a solution to the equation), so we can use this point to find the new y-intercept, b.
7 = 2*3 + b
b = 1
The perpendicular line is y = 2x + 1, and goes through point (3,7)