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ANSWER

Write an equation in slope intercept form of the line that passes through the given points . 1. (1, 4), (6, – 1). ANSWER. Y = -x + 5. 2. (-1, -2), (2, 7). ANSWER. Y = 3x + 1. Write an equation of a parallel line. EXAMPLE 1.

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ANSWER

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  1. Write an equation in slope intercept form of the line that passes through the given points. 1. (1, 4), (6, –1) ANSWER Y = -x + 5 2.(-1, -2), (2, 7) ANSWER Y = 3x + 1

  2. Write an equation of a parallel line EXAMPLE 1 Write an equation of the line that passes through (–3, –5) and is parallel to the liney = 3x – 1. SOLUTION STEP1 Identify the slope. The graph of the given equation has a slope of 3. So, the parallel line through (–3, –5) has a slope of 3. STEP2 Find the y-intercept. Use the slope and the given point.

  3. Write an equation of a parallel line EXAMPLE 1 y=mx+b Write slope-intercept form. –5=3(–3) +b Substitute3form,3for x,and5fory. Solve forb. 4 = b STEP3 Write an equation. Usey = mx + b. Substitute3formand4forb. y = 3x + 4

  4. 1. Write an equation of the line that passes through (–2, 11) and is parallel to the liney =–x + 5. ANSWER y = –x + 9 for Example 1 GUIDED PRACTICE

  5. SOLUTION Find the slopes of the lines. Line a: The equation is in slope-intercept form.The slope is 5. Determine whether lines are parallel or perpendicular EXAMPLE 2 Determine which lines, if any, are parallel or perpendicular. Line a: y = 5x – 3 Line b:x + 5y = 2 Line c:–10y – 2x = 0 Write the equations for lines band cin slope-intercept form.

  6. Lineb: x + 5y = 2 – x y = + 1 2 1 Linec: –10y – 2x = 0 5 5 5 x – y = Determine whether lines are parallel or perpendicular EXAMPLE 2 5y = – x + 2 –10y = 2x

  7. ANSWER Lines band chave slopes of – , so they are parallel. Lineahas a slope of5,the negative reciprocal of – , so it is perpendicular to lines band c. 1 1 5 5 Determine whether lines are parallel or perpendicular EXAMPLE 2

  8. ANSWER parallel: b and c; perpendicular: a and b, a and c for Example 2 GUIDED PRACTICE Determine which lines, if any, are parallel or perpendicular. Line a: 2x + 6y =–3 Line b: y = 3x – 8 Line c:–1.5y + 4.5x = 6

  9. STATE FLAG The Arizona state flag is shown in a coordinate plane. Lines aand bappear to be perpendicular. Are they? Determine whether lines are perpendicular EXAMPLE 3 Linea:12y = –7x + 42 Lineb:11y = 16x – 52 SOLUTION Find the slopes of the lines. Write the equations in slope-intercept form.

  10. 7 16 7 16 11 12 11 12 x y=– + 52 42 11 12 x y = – ANSWER The slope of line ais –. The slope of line bis . The two slopes are not negative reciprocals, so lines aand bare not perpendicular. Determine whether lines are perpendicular EXAMPLE 3 Linea:12y = –7x + 42 Lineb:11y = 16x – 52

  11. Identify the slope. The graph of the given equation has a slope of 2. Because the slopes of perpendicular lines are negative reciprocals, the slope of the perpendicular line through (4, –5) is . 1 2 – EXAMPLE 4 Write an equation of a perpendicular line Write an equation of the line that passes through(4, –5)and is perpendicular to the liney = 2x + 3. SOLUTION STEP1

  12. y= mx+b 1 – (4) +b –5= Substitute – for m, 4 for x, and –5 for y. 2 1 2 –3= b 1 2 1 y = – x – 3 Substitute – formand–3for b. 2 Write an equation of a perpendicular line EXAMPLE 4 STEP 2 Find the y-intercept. Use the slope and the given point. Write slope-intercept form. Solve for b. STEP3 Write an equation. y = mx + b Write slope-intercept form.

  13. ANSWER 1 No; the slope of line ais –, the slope of line bis . The slopes are not negative reciprocals so the lines are not perpendicular. 2 3 2 for Examples 3 and 4 GUIDED PRACTICE 3. Is line a perpendicular to line b?Justify your answer using slopes. Linea:2y +x = –12 Lineb:2y = 3x – 8

  14. 1 4 y = – x + 4 ANSWER for Examples 3 and 4 GUIDED PRACTICE 4. Write an equation of the line that passes through (4, 3) and is perpendicular to the line y = 4x – 7.

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