1 / 14

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.

roland
Télécharger la présentation

ANSWER

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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.

More Related