What is the slope-intercept form of the line passing through # (-6, 8)# and #(-3, 5) #?

1 Answer
Dec 7, 2017

Answer:

#y=-x+2#

Explanation:

Alright, so this is a two-part question. First we need to find the slope, then we need to find the y-intercept. Finally we plug all this into the slope intercept equation #y=mx+b#

The slope is commonly referred to as #m=(rise)/(run)# this can also be expressed as #m=(y_2-y_1)/(x_2-x_1)# by using the change in #y# and the change in #x#.

#m=(5-8)/(-3-(-6))#

#m=(-3)/3#

#color(red)(m=-1)#

Alright, now lets find the y-intercept by using that slope. If we plug that slope into the base formula we get #y=-x+b#. Since we already know one point, lets put #(-3, 5)# into that equation and solve for #b#.

#5=-(-3)+b#

#5-3=3+b-3#

#color(red)(2=b)#

Now is if plug out #b# into out equation, we get a finally answer of #color(red)(y=-x+2)#

Even though we're done, lets check it by putting in the other point.

#8=-(-6)+2#

#8-6=6+2-6#

#color(red)(2=2)#

Hope this helps!
~Chandler Dowd