# How do you write an equation of a line that passes through (4,9) , (-2,-6)?

Apr 3, 2015

I will use the point-slope form of a line ($y - {y}_{1} = m \left(x - {x}_{1}\right)$):

Point 1 will be (4,9)
Point 2 will be (-2,-6)

Calculating the slope: m=(∆y)/(∆x)=(y_2-y_1)/(x_2-x_1)=(9-(-6))/(4-(-2))=(9+6)/(4+2)=15/6=(3(5))/(3(2))=color(red)(5/2)

So: $y - \left(9\right) = \left(\frac{5}{2}\right) \left(x - 4\right)$

Now, I will transform the equation from point-slope to slope-intercept ($y = m x + b$) form. Remember, changing the form of a line's equation does not change the line. It simply rewrites the variables in a different way.

$y - \left(9\right) = \left(\frac{5}{2}\right) \left(x - 4\right)$
$y = \left(\frac{5}{2}\right) \left(x - 4\right) + 9$
$y = \frac{5}{2} x - \frac{20}{2} + 9$
$y = \frac{5}{2} x - 10 + 9$
$y = \frac{5}{2} x - 1$