Question

Write an equation in point-slope AND slope-intercept form of the equation of the line through the given points. Through: (5, -2) and (3, -4)

Answer 1

The first step is to determine the slope.

m = ( y2-y1)/(x2-x1)

m = ( -4 - -2)/( 3 - 5)

= (-4+2)/( 3-5)

= -2 / -2

= 1

Point slope form of the equation

y-y1 = m(x-x1) where m is the slope and (x1,y1) is a point on the line

y - -2 = 1(x -5)

y+2 = x-5

or

y - -4 = 1(x-3)

y+4 = x-3

To change this to slope intercept form y= mx+b where m is the slope and b is the y intecept

Subtract 4 from each side

y+4-4 = x-3-4

y = x-7

We can also do it with the first equation

y+2-2 = x-5-2

y = x-7