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

1 Answer
Psykolord1989 .
Mar 17, 2017

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

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