Write an Equation Given Two Points
Key Questions

Slope Formula
The slope formula of the line passing through the points
#(x_1,y_1)# and#(x_2,y_2)# can be found by:#m={y_2y_1}/{x_2x_1}# So to find the slope of a line segment joining the points ( 2,  5) and ( 2, 4).
First, label the points as
#x_1# = 2,#y_1# =  5,#x_2# = 2 and#y_2# = 4#m={y_2y_1}/{x_2x_1}# =#{4 5}/{2 2}# =#{9}/{4}# =#{9}/{4}# So, the slope (
#m# ) = 9/4. 
No, it does not as long as the point is on the line. You will end up with the same value for the
#y# intercept.
I hope that this was helpful.

If the slope of a line is undefined, then the line is a vertical line, so it cannot be written in slopeintercept form, but it can be written in the form:
#x=a# , where#a# is a constant.
Example
If the line has an undefined slope and passes through the point
#(2,3)# , then the equation of the line is#x=2# .
I hope that this was helpful.

Answer:
Use the differences in the y and x values to find the slope then substitute the values of one point into the equation to find b the y intercept.
Explanation:
Slope =
#( y_1y_2)/(x_1x_2)=m# By putting the x and y values for the two points into the slope equation the value for m can be found.
The equation of a line in the slope intercept form is
# y = mx +b # After finding m using the slope equation substitute one set of point values for y and x. This leaves b as the only unknown. Slope the resulting equation for b.
Questions
Forms of Linear Equations

Write an Equation Given the Slope and a Point

Write an Equation Given Two Points

Write a Function in SlopeIntercept Form

Linear Equations in PointSlope Form

Forms of Linear Equations

Applications Using Linear Models

Equations of Parallel Lines

Equations of Perpendicular Lines

Families of Lines

Fitting Lines to Data

Linear Interpolation and Extrapolation

Problem Solving with Linear Models

Dimensional Analysis