2x + y = 5; (7, 5)

Answer 1

plug x= 7 and y = 5 into the equation gives 2(7) + 5 = 19 which doesn't equal 5

the point is not on the line in that equation.

Maybe you're asking how far is the point from the line?

y=-2x +5. It's slope = -2, the slope of a perpendicular line is the negative inverse, +1/2

the perpendicular gives the distance from the line to the point, it's equation

is

y=x/2 + b. Plug in the point to find b. 5=7/2 + b. b= 5-7/2 = 3/2

the perpendicular equation is y= x/2 + 3/2

check where the perpendicular intersects the given equation

y= x/2 + 3/2 = 2x+5, solve for x

multiply by 2 to get

x + 3 = 4x +10

3x = -7

x = -7/3

y=2x+5 = 2(7/3) +5 = 14/3+5 = 29/3

now we need the distance from (-7/3, 29/3) to the original point (7,5)

d^2 = sum of change in y squared + change in change in x squared = 29^2/9 + 49/9 = 850/9

d = sqr(850/9) = (1/3)sqr850=29.155 = 29.155/3 = 0.8835 = distance from line to point