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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