Answer:
Step-by-step explanation:
The "unit rate" is the slope of the line, or the ratio of change in y to change in x.
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The "unit rate" of the relationship in the table can be found from the slope formula:
m = (y2 -y1)/(x2 -x1)
m = (16 -8)/(14 -7) = 8/7
The slopes of the various lines are conveniently found using the fact that they all terminate on grid points with y=6, and they all go through the origin. Their slope is the ratio of 6 to the x-coordinate of the termination point:
line 1: 6/2 = 3 . . . . slope not < 2
line 2: 6/3 = 2 . . . . slope not < 2
line 3: 6/4 = 3/2 . . . . slope < 2, > 8/7
line 4: 6/5 . . . . slope < 2, > 8/7
line 5: 6/6 = 1 . . . . slope not > 8/7
Lines 3 and 4 have slopes in the required range.
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<em>Alternate solution</em>
We can find the values of x corresponding to the limits on slope when y = 6. This lets us compare the given lines to the desired range of slope in a fairly direct way.
For the proportional relations shown,
y = mx
Then x = y/m, and we have, for y=6, ...
x = 6/2 = 3 . . . . upper limit on slope
x = 6/(8/7) = 42/8 = 5 1/4 . . . . lower limit on slope
The lines that terminate at points with y=6 and 3 < x < 5 1/4 are ...
lines 3 and line 4
