Meet Slope

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Discover Slope.

(A). Interact with the vertices of triangle to discover when the slope is positive, negative, zero, and undefined.

(B). Check the “slope” box in the applet and then interact with the line to discover when its slope of the dark line is positive, negative, zero, and undefined.

(C). Draw two lines with slope 3. What do you notice about the two lines?

What do you notice about the lines?

(D). Draw two lines with slope . What do you notice about the two lines?

(D). Draw two lines with slope . What do you notice about the two lines?

As we learn more about lines, we will occasionally have to consider perfectly vertical lines as a special case and treat them differently. Think about applying what you have learned in the last couple of activities to the case of vertical lines.

What is the same?

What is different?

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Investigating Slope.

(A). The figure shows three right triangles, each with its longest side on the same line.

(1). Explain why the three triangles are similar.

(2). Complete the table.

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Matching a Line with a Slope.

Here in the applet below are several lines.

Match each line shown with a slope.

One of the given slopes does not have a line to match. Draw a line with this slope on the empty grid below.

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Of the three lines in the graph, one has slope 1, one has slope 2, and one has slope . Label each line with its slope.

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Draw three lines with slope 2, and three lines with slope . What do you notice?

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The figure shows two right triangles, each with its longest side on the same line.

(1). Explain how you know the two triangles are similar.

(2). How long is XY ?

(3). For each triangle, calculate (vertical side)  (horizontal side).

(4). What is the slope of the line? Explain how you know.