Lesson 5 6 Parallel and Perpendicular Lines Parallel
- Slides: 12
Lesson 5. 6 Parallel and Perpendicular Lines § Parallel lines have the same slope § Perpendicular lines are opposite reciprocals. To find their slopes, you flip the number and change the sign.
Write the slope-intercept form of an equation for the line that passes through (4, – 2) and is parallel to the graph of The line parallel to Replace m with point-slope form. has the same slope, and (x, y) with (4, -2) in the
Point-slope form Replace m with y with – 2, and x with 4. Simplify. Distributive Property Subtract 2 from each side.
Write the equation in slopeintercept form. Answer: The equation is
Check You can check your result by graphing both equations. The lines appear to be parallel. The graph of passes through (4, – 2).
Write the slope-intercept form for an equation of a line that passes through (4, – 1) and is perpendicular to the graph of Step 1 Find the slope of the given line. Original equation Subtract 7 x from each side. Simplify.
Divide each side by – 2. Simplify. Step 2 The slope of the given line is So, the slope of the line perpendicular to this line is the opposite reciprocal of or
Step 3 Use the point-slope form to find the equation. Point-slope form and Simplify. Distributive Property
Subtract 1 from each side. Simplify. Answer: The equation of the line is
Check You can check your result by graphing both equations on a graphing calculator. Use the CALC menu to verify that passes through (4, – 1).
Write the slope-intercept form for an equation of a line perpendicular to the graph of and passes through (0, 6). Step 1 Find the slope of Original equation Subtract 5 x from each side. Simplify.
a. Write the slope-intercept form of an equation for the line that passes through (2, 3) and is parallel to the graph of b. Write the slope-intercept form for an equation of a line that passes through (– 3, 6) and is perpendicular to the graph of c. Write the slope-intercept form for an equation of a line perpendicular to the graph of and passes through the x-intercept of that line.
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