Writing Equations of Lines

Consider the graphed line.

Mai uses Triangle A and says the slope of this line is  . Elena uses Triangle B and says no, the slope of this line is 1.5. Do you agree with either of them? Explain.

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Writing the equation of a straight line when the slope and the intercept are given.

(A). In the following exercise, find any two points C and D. To do this, substitute any value of x in the given equation, to find the corresponding value of y. This gives you the coordinates of C. Do this step again with a different value of x to obtain coordinates for D.

Then, adjust A and B on the given line to the values of C and D that you obtained.

Click New Line to try another one.

(B). Enter the slope and intercept, and check the box to verify your answer.

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Establishing Slope Expressions.

(A). Complete the diagram in the applet below so that the vertical and horizontal segments have expressions for their lengths.

(B). Complete the diagram in the applet below so that the vertical and horizontal segments have expressions for their lengths.

(C). Line j is shown in the coordinate plane.

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Finding the Slope of a Line Through two Points.

(A). For each pair of points, find the slope of the line that passes through both points. If you get stuck, try plotting the points using this applet and drawing the line through them.

(B). Line is shown in the coordinate plane.

(1). What are the coordinates of points B ?
(1). What are the coordinates of points B ?

(2). What are the coordinates of points D ?

(6). Write a rule that would allow you to test whether (x, y)  is on line .

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Find each of the following and explain your reasoning:

(1). The length of segment  BE.

(2). The coordinates of  F.

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Consider the graphed linebelow.

(1). Mai uses Triangle A and says the slope of this line is  . Elena uses Triangle B and says no, the slope of this line is 1.5. Do you agree with either of them?

(2). Explain.