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Point-Slope Form of a Linear Equation Learn the point-slope form of an equation of a line Write equations in point-slope form that model real-world data

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You have been writing equations of the form y = a + bx. When you know the lines slope and the y-intercept you can write its equation directly in intercept form. But there are times that we dont know the y- intercept. Some homework questions had you work backwards from a point using the slope until you found the y-intercept. We can use the slope formula to generate the equation of a line from knowing the slope and one point on the line.

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Since the time Beth was born, the population of her town has increased at the rate of approximately 850 people per year. On Beths 9 th birthday the total population was nearly 307,650. If this rate of growth continues, what will be the population on Beths 16 th birthday?

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Because the rate of change is approximately constant, a linear equation should model this population. Let x = the time in years since Beths birth Let y = the population We know that the slope is 850 and one point is (9, 307,650) and another point on the straight line could be (x,y).

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Solving this equation yields: This equation models the growth of Beths town. Use it to find the population when Beth is 16. This equation form is called a point-slope form.

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If a line passes through (x 1, y 1 ) and has a slope of b, then the point-slope form of the equation is

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The Point-Slope Form for Linear Equations Page 235

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Silo and Jenny conducted an experiment in which Jenny walked at a constant rate. Unfortunately, Silo recorded on the data shown in the table. Elapse Time (s) Distance to the Walker (m)

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Silo and Jenny conducted an experiment in which Jenny walked at a constant rate. Unfortunately, Silo recorded only the data shown in the table. Elapse Time (s) Distance to the Walker (m)

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Complete steps 1-5 with your group. Be prepared to share your thinking with the class. Elapse Time (s) Distance to the Walker (m)

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Consider a new set of data that describe how the temperature of a pot of water changed over time as it was heated. Some of the group should create a paper graph while others use their graphing calculator to create a scatter plot. Complete steps 6-8 with your group. Time (s) Temperature ( o C)

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For step 9, compare your graph to others in your group. Does one graph show a line that is a better fit than others. Explain. Time (s) Temperature ( o C)

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When do you use slope-intercept form and when do you use point-slope form? Is there a difference between the two? Explain how the two forms are similar and how they are different.

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