Teaching Notes 4.13: Writing a Linear Equation,
Given Two Points
Writing a linear equation when two points are given is often a difficult task for students. It
requires background knowledge for finding the slope, solving equations, and using
slope-intercept form.- Explain to your students that they can use two points to write an equation of a line. The first
step is to find the slope of a line. Depending on the abilities of your students, you may find it
helpful to review the slope formula:m=y 2 −y 1
x 2 −x 1- Review the slope-intercept form,y=mx+b,wheremstands for the slope andbstands for
they-intercept. Explain that students will substitute values form,x,andy,andthensolve
forb. - Note that the final equation should be written in slope-intercept form with variables forx
andy, and numbers formandb. - Review the information and example on the worksheet with your students. Emphasize that
either ordered pair could be substituted forxandy. If necessary, discuss the steps for solving
the equations.
EXTRA HELP:
Check your work by creating a graph. Plot the given two points and draw a line through them. This
line should have the same slope andy-intercept as your equation.ANSWER KEY:
(1)y= 4 x+ 5 (2)y=− 2 x+ 3 (3)y= 5 x− 10 (4)y=−x− 2
(5)y=1
2
x+ 4 (6)y=2
3
x− 3 (7)y=−1
4
x+ 6 (8)y=− 7 x+ 17
------------------------------------------------------------------------------------------
(Challenge)They are both correct. The equationsy=xandy=x+0 are equivalent,
althoughy=xis the preferred form.
------------------------------------------------------------------------------------------162 THE ALGEBRA TEACHER’S GUIDE