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Writing Equations of Lines

Writing Equations of Lines. Equations of Lines. There are three main equations of lines that we use: Slope-Intercept – if you know the y-intercept and the slope, this is the quickest equation to use. y = mx + b, where m is the slope and b is the y-intercept. Equations of Lines.

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Writing Equations of Lines

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  1. Writing Equations of Lines

  2. Equations of Lines • There are three main equations of lines that we use: • Slope-Intercept – if you know the y-intercept and the slope, this is the quickest equation to use. • y = mx + b, where m is the slope and b is the y-intercept

  3. Equations of Lines • There are three main equations of lines that we use: • Point-Slope – if you know any point on the line (other than the y-intercept) and the slope, use this adaptation of the slope formula. • y – y1 = m(x – x1), where m is the slope and (x1, y1) is the known point

  4. Equations of Lines • There are three main equations of lines that we use: • Two Points – this isn’t really a separate equation. If you have two points, use the slope formula to find the slope, the write the equation using the Point-Slope form and either of the original points.

  5. Examples • Write an equation for the line shown.

  6. Examples • Write an equation of the line that passes through (-3,4) and has a slope of 2/3.

  7. Examples • Write an equation of the line that is perpendicular to the previous line (y = 2/3x + 6). • Write an equation of the line that is parallel to the previous line.

  8. Examples • Write an equation of the line that passes through (1,5) and (4,2).

  9. Real Life Examples • In 1970 there were 160 African-American women in elected public office in the United States. By 1993 the number had increased to 2332. Write a linear model for the number of African-American women who held elected public office at any given time between 1970 and 1993. Then use the model to predict the number of African-American women who will hold elected public office in 2010.

  10. Real Life Examples • The problem gave us two points – (1970,160) and (1993,2332). We can find the slope (or average rate of change of African-American women in elected office).

  11. Real Life Examples • Now, we need a verbal model, so we can develop a linear equation.

  12. Real Life Examples • Now, we need a verbal model, so we can develop a linear equation. • What are we looking for?

  13. Real Life Examples • Now, we need a verbal model, so we can develop a linear equation. • What are we looking for? • Number of office holders in 2010

  14. Real Life Examples • Now, we need a verbal model, so we can develop a linear equation. • So, number of office holders in general is the number we started with (160) plus the amount of increase every year (94.4) times the number of years between when we started and when we’re interested in (t). • OR

  15. Real Life Examples • y = 160 + 94.4t where y is the number of office holders and t is the numbers of years since 1970

  16. Direct Variation Equations • Two variables (x and y, for example) show a direct variation if y = kx and k ≠ 0. In this case k is called the constant of variation.

  17. Direct Variation Equations • Two variables (x and y, for example) show a direct variation if y = kx and k ≠ 0. In this case k is called the constant of variation. • To find the constant of variation, solve y = kx for k.

  18. Example • For example, a line goes through point (4,12) and x and y vary directly. What are the coordinates of another point on the line?

  19. Example • For example, a line goes through point (4,12) and x and y vary directly. What are the coordinates of another point on the line? • First, find k.

  20. Example • For example, a line goes through point (4,12) and x and y vary directly. What are the coordinates of another point on the line? • First, find k. y = kx

  21. Example • For example, a line goes through point (4,12) and x and y vary directly. What are the coordinates of another point on the line? • First, find k. y = kx 12 = k(4)

  22. Example • For example, a line goes through point (4,12) and x and y vary directly. What are the coordinates of another point on the line? • First, find k. y = kx 12 = k(4) 3 = k

  23. Example • For example, a line goes through point (4,12) and x and y vary directly. What are the coordinates of another point on the line? • Next, pick an x coordinate.

  24. Example • For example, a line goes through point (4,12) and x and y vary directly. What are the coordinates of another point on the line? • Finally, multiply that number times 3. This will give you the x (you picked it) and y (x * 3)coordinates of another point on this line.

  25. Identifying Direct Variation • The simplest way to test for direct variation is to divide each y coordinate by it’s corresponding x coordinate (that’s what we did to find k). If you get the same answer for each coordinate pair, the data shows direct variation.

  26. Example • Does this data show direct variation?

  27. Example • Does this data show direct variation?

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