Question

How do you write the point-slope form of an equation of the line that passes through each pair of points (4,1), (-3,6)?

Answer 1

point-slope form: `y-y_1=m(x-x_1) m=[slope](http://socratic.org/algebra/graphs-of-linear-equations-and-functions/slope) and (x_1,y_1)` is the point
slope-intercept form: `y=mx+c`

m(slope)=`tantheta=(y_2-y_1)/(x_2-x_1)=(6-1)/(-3-4)=-5/7`

therefore the equation to the line is:
y-1=(-5/7)(x-4)
`=>`7y-7= -5x+20
`=>` 5x+7y-27=0