Teaching Algebra with Manipulatives

Using Overhead Manipulatives
(Use with Algebra 1, Lesson 5-5)
Linear Equations in Point-Slope and Standard Forms
Objective Write linear equations in point-slope and standard forms.
Materials
• coordinate grid transparency*
• transparency pen*
• blank transparencies
* available in Overhead Manipulative Resources
Demonstration 1
Writing an Equation of a Line
• Copy the graph shown at the right on the coordinate grid
transparency.
• Tell students that you want to write an equation for the line.
Ask them to name the coordinates of S. 1,2 Then ask them
to find the slope of the line. 3 2
y
O
S
x
• Write
y 2
y 1
x2 x 1
m on a blank transparency.
Substitute the coordinates of S for x 1
and y 1
, and 3 for m.
2
Ask students to simplify the equation so it is in the form
y y 1
m(x x 1
).
y y
Substitute (x, y) for (x 2
, y 2
); 1
m.
x x1
Multiply each side by (x x 1
); y y 1
m(x x 1
). (y 2) 3 (x 1)
2
• Tell students that this is the point-slope form of a linear equation.
Ask what you know about the line from this form of the equation.
the coordinates of one point on the line and the slope of the line
• Remind students that the standard form of a line is in the form
Ax By C where A, B and C are real numbers and A and B are not
both zero. (Usually A and B are integers and A 0.) Show them how to
write the equation of the line in standard form. Multiply each side by 2;
use the distributive property; subtract 3x from each side; add 4 to each
side; multiply by 1; the standard form is 3x 2y 1.
• Have students repeat the process using a different point on the line. Ask
whether the same equation results from using the coordinates of any
point on the line. yes
© Glencoe/McGraw-Hill 100 Teaching Algebra with Manipulatives