which equation has both points?

Question

In the xy−coordinate plane shown below, point P has coordinates (8, −6). Which of the following is an equation of the line that contains points O and P?

y=-x+4

y=4 over 3*x

y=x-4

y=-3over4*x

Answer 1

If O is the origin with coordinates (0,0) then the slope of the line that contains points O and P is given by  

 

m = (y₂ - y₁) / (x₂ - x₁) = (-6 - 0) / (8 - 0) = -6/8 = -3/4  

 

So the equation is of the form  y = -(3/4)x + b  

 

Since the point (0,0) is on the line it must be true that  0 = -(3/4)*0 + b  ==>  b = 0  

 

So the equation of the line is  y = -(3/4)*x  

 

Alternatively you could just plug in the coordinates of point P into each of the choices and note that only the last choice works