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6-5 Point Slope Form

6-5 Point Slope Form. You will be learning 3 different forms (or formats) for writing linear equations. Slope-intercept form Standard form Point-slope form. Point Slope Form y – y 1 = m (x – x 1 ). m is the slope of the line and ( x 1 , y 1 ) is a point on the line.

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6-5 Point Slope Form

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  1. 6-5 Point Slope Form

  2. You will be learning 3 different forms (or formats) for writing linear equations. • Slope-intercept form • Standard form • Point-slope form

  3. Point Slope Form y – y1 = m(x – x1) m is the slope of the line and (x1 ,y1) is a point on the line

  4. When an equation is written in point slope form, you can identify the slope and a point. Ex. y - 4 = 2(x - 3) y – y1 = m(x – x1) So, the slope of the line is 2 and the point (3,4) is on the line…now it’s easy to graph!

  5. When an equation is written in point slope form, you can identify the slope and a point. Ex. y + 4 = 2(x + 3) y – y1 = m(x – x1) WATCH OUT FOR THE SIGNS So, the slope of the line is 2 and the point (-3,-4) is on the line…now it’s easy to graph!

  6. If you’re given a point and the slope of a line, it’s easy to write the equation. Remember to watch the signs!! Ex. Write an equation of the line that has a slope of -2 and passes through the point (-1,7) Since you are given a point and the slope, use the point slope form y – y1 = m(x – x1) x1 = -1 y1 = 7 m= -2 y – 7= -2(x – (-1)) Simplify y -7= -2(x + 1)

  7. If all you know is 2 points which the line passes through, can you use the point slope form? Yes! Just calculate the slope first, then use one of the points and the slope and put the equation in the point slope form. Ex. Write an equation for the line which passes through the points (2,5) and (4,6) y – y1 = m(x – x1) x1 = 2 y1 = 5 m= 1/2 y – 5 = 1/2(x – 2)

  8. How can you identify if two sets of data have a linear relationship? If there is a constant rate of change, or a slope, then it is linear. Now compare: change in y change in x 4 2 6 2 1 3 Since the rate of change is constant…1/2, the relationship is linear.

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