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Identify all the lines on the graph with unit rates that are less than 2 and greater than the unit rate of the relationship in the table.

x y
7 8
14 16
21 24
line 1
line 2
line 3
line 4
line 5

Identify all the lines on the graph with unit rates that are less than 2 and greater-example-1

2 Answers

10 votes

Answer:

line 3, line 4 :)

Explanation:

User Nurys
by
8.3k points
3 votes

Answer:

  • line 3
  • line 4

Explanation:

The "unit rate" is the slope of the line, or the ratio of change in y to change in x.

__

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.

_____

Alternate solution

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

User Andrey Tsarev
by
8.5k points

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