How do you write an equation in slope intercept form for the line through the given point (5, -2) and (-16, 4)?

1 Answer
Mar 25, 2015

The slope of your line is: #m=(Deltay)/(Deltax)=(y_2-y_1)/(x_2-x_1)# and represents the inclination of your line (change in #y# for a change in #x#).

In your case you have: #m=(4-(-2))/(-16-5)=6/-21=-2/7#

you can now insert this slope into the relationship:

#y-y_0=m(x-x_0)# that gives the equation of your line using, for example, the coordinates of your first point as:

#y-(-2)=-2/7(x-5)#

giving: #y=(-2/7)x-(4/7)#

So you have a line of slope #m=-2/7# and intercept at #y=-4/7#