#### Transcript Perpendicular Line Through a Given Point

• Write an equation of the line that passes through a given point, parallel to a given line. • Write an equation of the line that passes through a given point, perpendicular to a given line. • parallel lines • perpendicular lines 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 Parallel Line Through a Given Point Point-slope form Replace m with y with –2, and x with 4. Simplify. Distributive Property Subtract 2 from each side Parallel Line Through a Given Point Write the equation in slopeintercept form. Answer: The equation is 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. 0% D A 0% B C D C D. A 0% A. 0%B. C. D. B C. Determine Whether Lines are Perpendicular GEOMETRY The height of a trapezoid is measured on a segment that is perpendicular to a base. In trapezoid ARTP, RT and AP are bases. Can EZ be used to measure the height of the trapezoid? Explain. Determine Whether Lines are Perpendicular Find the slope of each segment. Determine Whether Lines are Perpendicular Answer: The slope of RT and AP is 1 and the slope of EZ is –7. –7●1 –1. EZ is not perpendicular to RT and AP, so it cannot be used to measure height. The graph shows the diagonals of a rectangle. Determine whether JL is perpendicular to KM. A. JL is not perpendicular to KM. 1. 2. 3. A 0% 0% B C. Cannot be determined A B C 0% C B. JL is perpendicular to KM. Perpendicular Line Through a Given Point Write the slope-intercept form for an equation of a line that passes through (4, –1) and is perpendicular to the graph of 7x – 2y = 3. Step 1 Find the slope of the given line. 7x – 2y = 3 7x – 2y – 7x = 3 – 7x –2y = –7 + 3 Original equation Subtract 7x from each side. Simplify. Perpendicular Line Through a Given Point Divide each side by –2. Simplify. Step 2 Perpendicular Line Through a Given Point Step 3 Use the point-slope form to find the equation. Point-slope form Simplify. Distributive Property Perpendicular Line Through a Given Point Subtract 1 from each side. Simplify. Answer: The equation of the line is Write the slope-intercept form for an equation of a line that passes through (–3, 6) and is perpendicular to the graph of 3x + 2y = 6. A. B. C. D. 0% 1. 2. 3. 4. A B C D A B C D Perpendicular Line Through a Given Point Write the slope-intercept form for an equation of a line perpendicular to the graph of 2y + 5x = 2 that passes through (0, 6). Step 1 Find the slope of 2y + 5x = 2. 2y + 5x = 2 2y + 5x – 5x = 2 – 5x 2y = –5x + 2 Original equation Subtract 5x from each side. Simplify. Perpendicular Line Through a Given Point Divide each side by 2. Simplify. Step 2 Perpendicular Line Through a Given Point Step 3 Substitute the slope and the given point into the point-slope form of a linear equation. Then write the equation in slope-intercept form. Point-slope form Distributive Property Answer: The equation of the line is Write the slope-intercept form for an equation of a line perpendicular to the graph of y = 2x + 1 that passes through the x-intercept of that line. A. B. D. A B0% C D D 0% B A 0% A. B.0% C. D. C C.