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kozerog [31]
1 year ago
5

Need some help with table 2.Fill up tables of proportional relationships with missing Values.

Mathematics
1 answer:
schepotkina [342]1 year ago
5 0

Proportional Relationships

If the variables x and y are in a proportional relationship, then:

y = kx

Where k is the constant of proportionality that can be found as follows:

k=\frac{y}{x}

If we are given a pair of values (x, y), we can find the value of k and use it to fill the rest of the table.

For example, Table 1 relates the cost y of x pounds of some items. We are given the pair (2, 2.50). We can calculate the value of k:

k=\frac{2.50}{2}=1.25

Now, for each value of x, multiply by this factor and get the value of y. For example, for x = 3:

y = 1.25 * 3 = 3.75

This value is also given and verifies the correct proportion obtained above.

For x = 4:

y = 1.25 * 4 = 5

For x = 7:

y = 1.25 * 7 = 8.75

For x = 10:

y = 1.25 * 10 = 12.50

Now for table 2, we are given the pair (3, 4.5) which gives us the value of k:

k=\frac{4.5}{3}=1.5

Apply this constant for the rest of the table.

For x = 4:

y = 1.5 * 4 = 6

For x = 5:

y = 1.5 * 5 = 7.50

For x = 8:

y = 1.5 * 8 = 12

The last column doesn't give us the value of x but the value of y, so we need to solve for x:

y=k\cdot x\text{  }=>\text{ }x=\frac{y}{k}

For y = 15:

x=\frac{15}{1.5}=10

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<h3>Answer:  A) Parallel </h3>

===================================================

Explanation:

I've highlighted lines m and k in red (see diagram below). We'll ignore the other lines. On those red lines, I've added blue points with their coordinate locations.

Line m has point A = (-3, 5) and B = (-1, -3). Let's use the slope formula to find the slope through these points

m = (y2-y1)/(x2-x1)

m = (-3-5)/(-1-(-3))

m = (-3-5)/(-1+3)

m = -8/2

m = -4

The slope of line AB, aka line m, is -4.

-------------

Line k has points C = (1, 5) and D = (3, -3) on it. We'll use the slope formula to get...

m = (y2-y1)/(x2-x1)

m = (-3-5)/(3-1)

m = -8/2

m = -4

The slope of line CD, aka line k, is -4

---------------

Both lines m and k have the same slope of -4. Therefore, the two lines are parallel. Parallel lines always have the same slope, but different y intercepts. So these lines will never intersect one another.

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