Vocabulary parallel lines: lines that have the same slope perpendicular lines: lines whose slopes are negative (opposite) reciprocals of each other (their.

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Vocabulary parallel lines: lines that have the same slope perpendicular lines: lines whose slopes are negative (opposite) reciprocals of each other (their product is -1)

Example 1 Parallel Line Through a Given Point Write the slope-intercept form of an equation for the line that passes through (4, –2) and is parallel to the graph of

Example 1 Parallel Line Through a Given Point Point-slope form Simplify and use the Distributive Property Subtract 2 from each side. Replace m with y with –2, and x with 4.

Example 1 Parallel Line Through a Given Point Write the equation in slope-intercept form. Answer: The equation is

A.A B.B C.C D.D Example 1 Write the slope-intercept form of an equation for the line that passes through (2, 3) and is parallel to the graph of A. B. C. D.

Example 2A Slopes of Perpendicular Lines A. GEOMETRY The height of a trapezoid is the length of a segment that is perpendicular to both bases. In trapezoid ARTP, RT and AP are bases. Can EZ be used to measure the height of the trapezoid? Explain.

Example 2A Slopes of Perpendicular Lines Find the slope of each segment. Answer:The slope of RT and AP is 1 and the slope of EZ is –7. Since 1(–7) ≠ –1, EZ is not perpendicular to RT and AP. So, it cannot be used to measure the height of ARTP.

Example 2B Slopes of Perpendicular Lines B. GEOMETRY The height of a trapezoid is the length of a segment that is perpendicular to both bases. In trapezoid ARTP, RT and AP are bases. Are the bases parallel? Answer:Yes, both RT and AP have a slope of 1.

A.A B.B C.C Example 2 The graph shows the diagonals of a rectangle. Determine whether JL is perpendicular to KM. A.JL is not perpendicular to KM. B.JL is perpendicular to KM. C.cannot be determined FYI: The diagonals of a rhombus meet at right angles. The diagonals of a rectangle are equal in length

Example 3 Parallel or Perpendicular Lines Determine whether the graphs of x + 3y = 12, and 2x – 6y = –5 are parallel or perpendicular. Explain.

A.A B.B C.C D.D Example 3 A.y = –2x + 1 and x – 2y = –4 are perpendicular. None of the line are parallel. B.y = –2x + 1 and y = 3 are perpendicular. None of the line are parallel. C.y = –2x + 1 and x – 2y = –4 are parallel. None of the line are perpendicular. D.None of the lines are parallel or perpendicular. Determine whether the graphs of y = –2x + 1, x – 2y = –4, and y = 3 are parallel or perpendicular.

Example 4 Parallel Line Through a Given Point Step 1Find the slope of the given line by solving the equation for y. 7x – 2y=3 Original equation 7x – 7x – 2y=–7x + 3 Subtract 7x from each side. –2y=–7x + 3 Simplify. Divide each side by –2. Simplify. Write an equation in slope-intercept form for the line that passes through (4, –1) and is perpendicular to the graph of 7x – 2y = 3.

Example 4 Parallel Line Through a Given Point The slope is Step 2The slope of the perpendicular line is the opposite reciprocal of Find the equation of the perpendicular line. y – y 1 = m(x – x 1 )Point-slope form Simplify.

Subtract 1 from each side. Example 4 Parallel Line Through a Given Point Distributive Property Simplify. Answer:

A.A B.B C.C D.D Example 4 Write an equation in slope-intercept form for the line that passes through (–3, –2) and is perpendicular to the graph of x + 4y = 12. A. B. C. D.

Concept (opposite reciprocals)