Question

A line passes through A (-3,-2) and B (2,1) Does it also pass through the point C (5, 3)?

Answer 1

We calculate the equation of this line:
Point-slope form:
Given a point and the solope the point-slope form is:
y-y₀=m(x-x₀)

m=(y₂-y₁) / (x₂-x₁)

Data:
(-3,-2)
(2,1)

m=(1-(-2)) / (2-(-3))=3/5

y-y₀= m(x-x₀)
y-1=3/5(x-2)    (point-slope form)
y=3/5 x-6/5+1
y=3/5 x-1/5 (Slope-intercepted form)

The equation of this line is : y=3/5 x-1/5

Now , we check if the point C belongs this line:
(5,3) this means:  x=5 and y=3
Therefore:
y=3/5 (5)-1/5=3 - 1/5=(15-1)/5=14/5≠3

Answer: the point C doesn´t pass through this line.