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Writing Equations

Writing Equations. “I can write an equation of a line, given two points on the line.”. What do we already know?. An equation for a line has the form: . We need to know the to write the equation for the line. We also need the - intercept to complete the equation for a line.

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Writing Equations

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  1. Writing Equations • “I can write an equation of a line, given two points on the line.”

  2. What do we already know? • An equation for a line has the form: . • We need to know the to write the equation for the line. • We also need the - intercept to complete the equation for a line.

  3. The Slope Formula • If we know nothing else about the line, we can find its equation given two points on the line. • We’ll use the slope formula.

  4. Using the slope formula • Example 1: • Find the slope of the line through the points (-2, 4) and (5, -3).

  5. Using the slope formula • Practice: • Given the points, find the slope: • (1, -19) and (-2, -7) • (9, 3) and (19, -17)

  6. Once we have the slope, we need to complete the equation by finding the y-intercept (b). y = mx + b Finding the y-intercept • From the previous practice problem, with points (9, 3) and (19, -17). We found the slope (m) was -2. • Any ideas on how we can now find b?

  7. For our problem, we have two points (9, 3) and (19, -17) and slope of -2. • We need to use one of these points and the slope to solve for b. Finding the y-intercept y = mx + b y = -2x + b (using slope we already found) 3 = -2(9) + b (substitute in x and y from our points)

  8. For our problem, we have two points (9, 3) and (19, -17) and slope of -2. • We need to use one of these points and the slope to solve for b. Finding the y-intercept y = mx + b y = -2x + b (using slope we already found) 3 = -2(9) + b (substitute in x and y from our points) +18 +18 21 = b (solve for b) y = -2x + 21 Put it all together!

  9. Another Example • Find the equation for the line that goes through the point: (2, -7) and (4, 5) Step 1: Find the Slope Step 2: Put the Slope into the equation Step 3: Substitute (x,y) into the equation Step 4: Solve for b Step 5: Put it all together

  10. Practice • Find the equation for the lines that go through the following points: • (6, -12) and (15, -3) • (4, 3) and (2, 1)

  11. Closure In your own words, describe the steps to find the equation of a line given two points on the line.

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