Unit D: Graphing

Practice


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  1. Identify the graph as direct variation, partial variation, or neither. If the graph represents either direct variation or partial variation, calculate the slope.





  2. Identify the graph as direct variation, partial variation, or neither. If the graph represents either direct variation or partial variation, calculate the slope.





  3. Identify the table of values as direct variation, partial variation, or neither. If the table of values represents direct variation or partial variation, calculate the slope.

    x
    		y
    0 0
    5
    		5.5
    10
    		11
    20
    		16.5


  4. Identify the equation y = 2.7x + 0.81 as direct variation, partial variation, or neither. If the equation represents either direct variation or partial variation, calculate the slope.

  5. Identify the equation y = 100x as direct variation, partial variation, or neither. If the equation represents either direct variation or partial variation, calculate the slope.

  1. Identify the graph as direct variation, partial variation, or neither. If the graph represents either direct variation or partial variation, calculate the slope.





The graph has a y-intercept of 4 (the line intersects with the y-axis at point (0, 4)). Since the line is straight, this graph represents partial variation.

Let (0, 4) = (x1, y1) and (1, 5) = (x2, y2).

m = y 2 - y 1 x 2 - x 1 = 5 - 4 1 - 0 = 1 1 = 1

The slope, m, is 1.
Identify the graph as direct variation, partial variation, or neither. If the graph represents either direct variation or partial variation, calculate the slope.





The graph passes through point (0, 0), but it is not a straight line. The line graph does not represent direct variation or partial variation.
Identify the table of values as direct variation, partial variation, or neither. If the table of values represents direct variation or partial variation, calculate the slope.

x
y
0 0
5 5.5
10 11
20 16.5

The graph passes through the point (0, 0), however, the x-values and the y-values do not increase at the same rate. Therefore the rate of change is not constant. The graph represents neither direct variation nor partial variation.




Identify the equation y = 2.7x + 0.81 as direct variation, partial variation, or neither. If the equation represents either direct variation or partial variation, calculate the slope.

Since the equation is in the form y = mx + b, the equation represents partial variation, where the slope is 2.7 and the y-intercept is 0.81.
Identify the equation y = 100x as direct variation, partial variation, or neither. If the equation represents either direct variation or partial variation, calculate the slope.

Since the equation is in the form y = mx, the equation represents direct variation, where the slope is 100.