Math presentation551
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The document provides steps to find lines through a given point (4, -1) that are parallel and perpendicular to the given line 2x - 3y = 9. To find the parallel line, the slope of the given line is calculated as m = 2/3. The equation of the parallel line through the given point is then derived as y + 1 = (2/3)(x - 4). To find the perpendicular line, the slope is calculated as the negative reciprocal of the original slope, which is m = -3/2. The equation of the perpendicular line through the given point is then derived as y - (-1) = -3/2(x - 4).
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The document provides steps to find lines parallel and perpendicular to the given line 2x - 3y = 9 through the point (4, -1). It is given that the slope of the original line is 2/3. The parallel line has the same slope of 2/3, while the perpendicular line has the slope of the negative reciprocal -3/2. Equations for both the parallel and perpendicular lines through the given point are provided.
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- 2. âĸ Given the line 2x â 3y = 9 and the point (4, â1), find lines through the point that are âĸ (a) parallel to the given line and âĸ (b) perpendicular to it.
- 4. âĸ solve "2x â 3y = 9" for "y=", so that you can find the reference slope: âĸ 2x â 3y = 9Â Â Â Â Â â3y = â2x + 9Â Â Â Â Â Â Â Â Â y = ( 2/3)x â 3 The reference slope from the reference line is m = 2/3
- 5. âĸ Previous answer: slope m = 2/3 âĸ y â (â1) = ( 2/3 )(x â 4)y + 1 = ( 2/3 ) x â 8/3y = ( 2/3 ) x â 3 8 /3 â 3/3y = ( 2/3 ) x â 11/3 3
- 6. Step 3: perpendicular line
- 7. Resource Slide âĸ http://www.purplemath.com/modules/strtlneq3.htm âĸ http://www.ixl.com/math/standards/california/algebra-1 âĸ Butte County Regional Occupational Program. Career and Technical Education Online. Chico, Calif.: Butte County Office of Education. http://www.cteonline.org (accessed October 2004). âĸ California State Board of Education. Content Standards. http://www.cde.ca.gov/be/st/ss/ index.asp âĸ California State Board of Education. Curriculum Frameworks. http://www.cde.ca.gov/be/st/fr/ index.asp
- 8. âĸ (5.0) Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step. âĸ (6.0) Students graph a linear equation and compute the x- and y- âĸ (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. âĸ (10.0) Students add, subtract, multiply, and divide monomials and polynomials. Students solve multistep problems, including word problems, by using these techniques.