• Given the line 2x – 3y = 9 and the point (4, –

1), find lines through the point that are

• (a) parallel to the given line and

• (b) perpendicular to it.

• solve "2x – 3y = 9" for "y=", so that you can find the

reference slope:

• 2x – 3y = 9 –3y = –2x + 9 y = ( 2/3)x – 3

The reference slope from the reference line is m = 2/3

• Previous answer: slope m = 2/3

• y – (–1) = ( 2/3 )(x – 4)y + 1 = ( 2/3 ) x – 8/3y = ( 2/3 ) x

– 8/3 – 3/3y = ( 2/3 ) x – 11/3

Step 3: perpendicular line

• for the perpendicular slope; flip the slope and change the sign.

• perpendicular slope is m = – 3/2

• point-slope form:y – (–1) = ( – 3/2 )(x – 4)y + 1 = ( – 3/2 ) x+ 6y = ( – 3/2 ) x + 5

• Full Solution =

Resource Slide

• http://www.purplemath.com/modules/strtlneq3.htm

• http://www.ixl.com/math/standards/california/algebra-1

• Butte County Regional Occupational Program. Career and Technical Education Online. Chico, Calif.: Butte County Office of Education. http://www.cteonline.org (accessed October 2004).

• California State Board of Education. Content Standards. http://www.cde.ca.gov/be/st/ss/ index.asp

• California State Board of Education. Curriculum Frameworks. http://www.cde.ca.gov/be/st/fr/ index.asp

• (5.0) Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step.

• (6.0) Students graph a linear equation and compute the x- and y-

• (8.0) Students understand the concepts of parallel lines and perpendicular lines and how those slopes are related. Students are able to find the equation of a line perpendicular to a given line that passes through a given point.

• (10.0) Students add, subtract, multiply, and divide monomials and polynomials. Students solve multistep problems, including word problems, by using these techniques.