# How do you write an equation in slope-intercept form for a line-passing through A(4,-3) and B(10,5)?

Mar 17, 2017

$y = \left(\frac{4}{3}\right) x - \left(\frac{25}{3}\right)$

#### Explanation:

Recall that slope intercept form places the equation in the former $y = m x + b$, where my is the slope and is calculated by $\frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$. Here, that is (5+3)÷(10-4) = 8/6 = 4/3

For the y-intercept b, recall pt slope firm, $y - {y}_{1} = m \left(x - {x}_{1}\right)$. We can put everything but y on the right hand side (which is how we normally find slope intercept form), which yields $y = m x - m {x}_{1} + {y}_{1}$. Since slope intercept form gives us $y = m x + b$, then by substitution we can see that $b = - m {x}_{1} + {y}_{1}$. We will check both pts above to ensure b is the same for both.

${b}_{A} = - \left(\frac{4}{3}\right) 4 - \frac{9}{3} = - \frac{16}{3} - \frac{9}{3} = - \frac{25}{3}$
${b}_{B} = - \left(\frac{4}{3}\right) 10 + \frac{15}{3} = - \frac{40}{3} + \frac{15}{3} = - \frac{25}{3}$

The y-intercepts are equal; thus our equation for slope intercept form is

$y = m x + b = \left(\frac{4}{3}\right) x - \frac{25}{3}$