Relating Concepts For individual or group investigation Recall from Chap...

Relating Concepts For individual or group investigation

Recall from Chapter 1 that a unique line is determined by two distinct points on the line and that the values of m and b can then be determined for the general form of the linear function ƒ(x) = mx + b.

Work these exercises in order .

Fill in the blanks with the correct responses, based on your work in Exercises 81–87.

If the points with coordinates (x₁, y₁) and (x₂, y₂) lie on a line, then when we add the positive constant c to each y-value, we obtain the points with coordinates (x₁, y₁ + ________) and (x₂, y₂ + ________). The slope of the new line is the slope of the original line. The graph of the new line can be obtained by shifting the graph of the original line ________ units in the ________ direction.

Reference 81 to 87

81.Sketch by hand the line that passes through the points (1, -2) and (3, 2).

82. Use the slope formula to find the slope of this line.

83. Find the equation of the line, and write it in the form y₁ = mx + b.

84. Keeping the same two x-values as given in Exercise 81, add 6 to each y-value. What are the coordinates of the two new points?

85. Find the slope of the line passing through the points determined in Exercise 84.

86. Find the equation of this new line, and write it in the form y₂ = mx + b.

87. Graph both y1 and y2 in the standard viewing window of your calculator, and describe how the graph of y₂ can be obtained by vertically translating the graph of y_{1 .}What is the value of the constant in this vertical translation? Where do you think it comes from?