Step 1.
Find the slope using the equation m=(y_2-y_1)/(x_2-x_1)m=y2−y1x2−x1, where mm is the slope, and (x_1,y_1)(x1,y1) and (x_2,y_2)(x2,y2) are the two points on the line.
Example
Find the slope of a line passing through the points (color(red)(-2),color(blue)(-1))(−2,−1) and (color(red)(4),color(blue)(3))(4,3).
(color(red)(-2),color(blue)(-1))=(color(red)(x_1), color(blue)(y_1))(−2,−1)=(x1,y1)
(color(red)(4),color(blue)(3))=(color(red)(x_2),color(blue)(y_2))(4,3)=(x2,y2)
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))m=y2−y1x2−x1=3−(−1)4−(−2)=color(blue)(4)/color(red)6=color(purple)(2)/color(purple)346=23
Step 2.
Determine the point-slope form of a linear equation (y-y_1)=m(x-x_1)(y−y1)=m(x−x1), where (x_1,y_1)(x1,y1) 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)))(y−(−1))=23(x−(−2)) =
color(blue)(y)+color(blue)(1)=color(purple)(2/3)(color (red)(x)+color(red)(2))y+1=23(x+2)
Convert to slope-intercept form y=mx+by=mx+b, where mm is the slope and bb is the y-intercept, by solving for yy.
y+1=2/3x+2y+1=23x+2
Subtract 11 from both sides.
y=2/3x+2-1y=23x+2−1 =
y=2/3x+1y=23x+1
The slope intercept is 11.
