# Equations of All Kinds of Lines

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Determine the Equation of a Line From the Points on the Planes.

(A). Plot at least 10 points whose y-coordinate is -4.

(1). What do you notice about the points?

(2). Which equation makes the most sense to represent all of the points with -coordinate and -4 ?

(3). Explain how you know.

(B). Plot at least 10 points whose y-coordinate is 3.

(1). What do you notice about the points?

(2). Which equation makes the most sense to represent all of the points with -coordinate and 3 ?

(3). Explain how you know.

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Draw a Line From the Equation.

(1). Graph the equation x = -2.

(2). Graph the equation y = 5.

(3). Draw the rectangle with vertices (2, 1), (5, 1), (5, 3), (2,3).

For each of the four sides of the rectangle, write an equation for a line containing the side.

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Find the Coordinates of a Rectangle on a Coordinate Plane.

A rectangle has sides on the graphs of = -1, = -3, = -1, =1 . Find the coordinates of each vertex. You may use the applet below to help you.

There are many possible rectangles whose perimeter is 50 units.

(1). Complete the table with lengths, , and widths, , of such rectangles.

Each rectangle has a vertex that lies in the first quadrant. These vertices lie on a line.

(2). Draw in this line in the same applet above, and write an equation for it.

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The graph shows one rectangle whose perimeter is 50 units. Draw more rectangles with perimeter 50 units using the values from your table. Make sure that each rectangle has a lower left vertex at the origin and two sides on the axes.

(1). What is the the slope of this line?

(2). How does the slope describe how the width changes as the length changes (or vice versa)?

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Suppose you wanted to graph the equation = -4 – 1

(1). Describe the steps you would take to draw the graph.

(2). How would you check that the graph you drew is correct?

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Use the applet below to answer the next set of problems:

Draw the following lines and then write an equation for each.

(1). Slope is 0, -intercept is 5.

(2). Slope 2, -intercept = -1.

(3). Slope = – , -intercept = -1.