1 / 16

Write an equation given two points

12. – 3. 10 – (– 2). y 2 – y 1. =. m =. =. = – 4. x 2 – x 1. 2 – 5. EXAMPLE 4. Write an equation given two points. Write an equation of the line that passes through (5, –2) and (2, 10). SOLUTION. The line passes through ( x 1 , y 1 ) = (5,– 2) and

jameszamora
Télécharger la présentation

Write an equation given two points

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. 12 – 3 10 – (– 2) y2 – y1 = m= = = – 4 x2 –x1 2 –5 EXAMPLE 4 Write an equation given two points Write an equation of the line that passes through (5, –2) and (2, 10). SOLUTION The line passes through (x1, y1) = (5,– 2) and (x2, y2) = (2, 10). Find its slope.

  2. EXAMPLE 4 Write an equation given two points You know the slope and a point on the line, so use point-slope form with either given point to write an equation of the line. Choose (x1, y1) = (4, – 7). y2– y1=m(x –x1) Use point-slope form. y–10=–4(x –2) Substitute for m, x1, and y1. y –10 = – 4x + 8 Distributive property y = – 4x + 8 Write in slope-intercept form.

  3. EXAMPLE 5 Write a model using slope-intercept form Sports In the school year ending in 1993, 2.00 million females participated in U.S. high school sports. By 2003,the number had increased to 2.86 million. Write a linear equation that models female sports participation.

  4. EXAMPLE 5 Write a model using slope-intercept form SOLUTION STEP 1 Define the variables. Let x represent the time (in years) since 1993 and let yrepresent the number of participants (in millions). STEP 2 Identify the initial value and rate of change. The initial value is 2.00. The rate of change is the slope m.

  5. 2.86 – 2.00 0.86 = = 10 –0 10 y2 – y1 m= x2 –x1 EXAMPLE 5 Write a model using slope-intercept form Use (x1, y1) =(0, 2.00) and (x2, y2) = (10, 2.86). = 0.086 STEP 3 Write a verbal model. Then write a linear equation.

  6. y = 2.00 + 0.086 x ANSWER In slope-intercept form, a linear model is y = 0.086x + 2.00. EXAMPLE 5 Write a model using slope-intercept form

  7. – 7 – 5 y2 – y1 = m= = – 2 x2 –x1 4 –(– 2) for Examples 4 and 5 GUIDED PRACTICE GUIDED PRACTICE Write an equation of the line that passes through the given points. 6. (– 2, 5), (4, – 7) SOLUTION The line passes through (x1, y1) = (– 2, 5) and (x2, y2) = (4, – 7). Find its slope.

  8. for Examples 4 and 5 GUIDED PRACTICE GUIDED PRACTICE You know the slope and a point on the line, so use point-slope form with either given point to write an equation of the line. Choose (x1, y1) = (4, – 7). y– y1=m(x –x1) Use point-slope form. y–7 =–2(x –4) Substitute for m, x1, and y1. Simplify y – 7 = – 2 (x + 4) y + 7 = – 2x + 8 Distributive property y = – 2x + 1 Write in slope-intercept form.

  9. – 8 – 1 y2 – y1 – 9 = m= = = 1 – 9 x2 –x1 – 3 –6 for Examples 4 and 5 GUIDED PRACTICE GUIDED PRACTICE 7. (6, 1), (–3, –8) SOLUTION The line passes through (x1, y1) = (6, 1) and (x2, y2) = (–3, –8). Find its slope.

  10. for Examples 4 and 5 GUIDED PRACTICE GUIDED PRACTICE You know the slope and a point on the line, so use point-slope form with either given point to write an equation of the line. Choose (x1, y1) = (– 3, – 8). y – y1=m(x – x1) Use point-slope form. y – (– 8))=1(x – (– 3)) Substitute for m, x, and y1. y +8 = 1 (x + 3) Simplify y +8 = x + 3 Distributive property y = x – 5 Write in slope-intercept form.

  11. 0 – 2 y2 – y1 2 = – m= = 11 x2 –x1 10– (–1) for Examples 4 and 5 GUIDED PRACTICE GUIDED PRACTICE 8. (–1, 2), (10, 0) SOLUTION The line passes through (x1, y1) = (– 1, 2) and (x2, y2) = (10, 0). Find its slope.

  12. 2 – y – 0=(x – 10) 11 2 – y = (x – 10) 11 20 2 – y = x + 11 11 20 2 – x + = 11 11 for Examples 4 and 5 GUIDED PRACTICE GUIDED PRACTICE You know the slope and a point on the line, so use point-slope form with either given point to write an equation of the line. Choose (x1, y1) = (10, 0). y – y1=m(x – x1) Use point-slope form. Substitute for m, x, and y1. Simplify Distributive property Write in slope-intercept form.

  13. for Examples 4 and 5 GUIDED PRACTICE GUIDED PRACTICE 9. Sports In Example 5, the corresponding data for males are 3.42 million participants in 1993 and 3.99 million participants in 2003. Write a linear equation that models male participation in U.S. high school sports.

  14. for Examples 4 and 5 GUIDED PRACTICE GUIDED PRACTICE SOLUTION STEP 1 Define the variables. Let x represent the time (in years) since 1993 and let yrepresent the number of participants (in millions). STEP 2 Identify the initial value and rate of change. The initial value is 3.42. The rate of change is the slope m.

  15. 3.99 – 3.42 = 10 –0 y2 – y1 m= x2 –x1 for Examples 4 and 5 GUIDED PRACTICE GUIDED PRACTICE Use (x1, y1) =3.42 and (x2, y2) =3.99 = 0.057 STEP 3 Write a verbal model. Then write a linear equation.

  16. y = 3.42 + 0.057 x ANSWER In slope-intercept form, a linear model is y = 0.057x + 3.42 for Examples 4 and 5 GUIDED PRACTICE GUIDED PRACTICE

More Related