How do you write an equation of a line going through (2,1) and (-2,-1)?

Recall that the general equation for a line is:

#color(teal)(|bar(ul(color(white)(a/a)y=mx+bcolor(white)(a/a)|)))#

where:
#y=#y-coordinate
#m=#slope
#x=#x-coordinate
#b=#y-intercept

Determining the Equation of the Line
#1#. Start by labelling the coordinates to either be coordinate #1# or #2#.

Coordinate #1#: #(color(red)(x_1),color(teal)(y_1))=(color(red)2,color(teal)1)#

Coordinate #2#: #(color(blue)(x_2),color(darkorange)(y_2))=(color(blue)(-2),color(darkorange)(-1))#

#2#. Find the slope between the two coordinates using the formula, #m=(y_2-y_1)/(x_2-x_1)#.

#m=(color(darkorange)(y_2)-color(teal)(y_1))/(color(blue)(x_2)-color(red)(x_1))#

#m=(color(darkorange)(-1)-color(teal)1)/(color(blue)(-2)-color(red)2)#

#m=(-2)/(-4)#

#color(violet)(m=1/2)#

#3#. Find the value of the y-intercept by substituting the slope and either coordinate #1# or #2# into #y=mx+b#. In this case, we will use coordinate #1#.

#y=mx+b#

#color(teal)1=color(violet)(1/2)(color(red)2)+b#

#1=1+b#

#b=0#

#4#. Rewrite the equation.

#color(green)(|bar(ul(color(white)(a/a)y=1/2xcolor(white)(a/a)|)))#