Step 1.
Find the slope using the equation #m=(y_2-y_1)/(x_2-x_1)#, where #m# is the slope, and #(x_1,y_1)# and #(x_2,y_2)# are the two points on the line.
Example
Find the slope of a line passing through the points #(color(red)(-2),color(blue)(-1))# and #(color(red)(4),color(blue)(3))#.
#(color(red)(-2),color(blue)(-1))=(color(red)(x_1), color(blue)(y_1))#
#(color(red)(4),color(blue)(3))=(color(red)(x_2),color(blue)(y_2))#
#color(purple)m=(color(blue)(y_2)-color(blue)(y_1))/(color(red)(x_2)-color(red)(x_1))=(color(blue)(3)-(color(blue)(-1)))/(color(red)(4)-(color(red)(-2))#=#color(blue)(4)/color(red)6=color(purple)(2)/color(purple)3#
Step 2.
Determine the point-slope form of a linear equation #(y-y_1)=m(x-x_1)#, where #(x_1,y_1)# is one of the points.
Continue with the previous example.
#(color(blue)(y)-(color(blue)(-1)))=color(purple)(2/3)(color(red)(x)-(color(red)(-2)))# =
#color(blue)(y)+color(blue)(1)=color(purple)(2/3)(color (red)(x)+color(red)(2))#
Convert to slope-intercept form #y=mx+b#, where #m# is the slope and #b# is the y-intercept, by solving for #y#.
#y+1=2/3x+2#
Subtract #1# from both sides.
#y=2/3x+2-1# =
#y=2/3x+1#
The slope intercept is #1#.
