Question

What is the equation of the line that passes through points `(1,4)` and `(3,2)`?

How do you write it in slope-intercept and general form?

Answer 1

`f(x)=-x+5`

Explanation:

Since the question speaks of a line, we assume that this is a linear function that follow the generic equation `f(x)=ax+b`, where `f(x)=y` and `a` and `b` are coefficients . We may begin by extraction the values for `x` and `y` from the points given and make a system of equations:

`{4=a+b`
`{2=3a+b`

This system can be solved by two ways. I'm going show it using the substitution method, but the additive method works as well. Therefore, isolate either `a` or `b` in the first equation:

`{4=a+b => b=4-a`
`{2=3a+b`

Then substitute it in the other equation:

`2=3a+(4-a)`
`2=2a+4`
`2a=-2`
`a=-1`

Since `b=4-a`, then `b=4-(-1)=5`

Notice that the negative sign of `a` was expected, since the function is downwards inclined. For making the final answer, lets substitute the coeficients `a` and `b` in the gerenal equaion:

`f(x)=-x+5`