Question

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

Answer 1

`y=(4/3)x-(25/3)`

Explanation:

Recall that slope intercept form places the equation in the former `y=mx+b`, where my is the slope and is calculated by `(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(x-x_1)`. We can put everything but y on the right hand side (which is how we normally find slope intercept form), which yields `y=mx-mx_1+y_1`. Since slope intercept form gives us `y=mx+b`, then by substitution we can see that `b=-mx_1+y_1`. We will check both pts above to ensure b is the same for both.

`b_A = -(4/3)4 -9/3=-16/3-9/3=-25/3`
`b_B = -(4/3)10 +15/3=-40/3+15/3=-25/3`

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

`y=mx+b=(4/3)x-25/3`