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?

May 30, 2016

$f \left(x\right) = - x + 5$

Explanation:

Since the question speaks of a line, we assume that this is a linear function that follow the generic equation $f \left(x\right) = a x + b$, where $f \left(x\right) = y$ 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:

$2 = 3 a + \left(4 - a\right)$
$2 = 2 a + 4$
$2 a = - 2$
$a = - 1$

Since $b = 4 - a$, then $b = 4 - \left(- 1\right) = 5$

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:

$f \left(x\right) = - x + 5$