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.
