We can see that the distance between the two points in Quantity A is 4 because they have the same y-coordinate and x-coordinates that are 4 apart (10 – 6).

Quantity B is a little trickier to figure out and requires either the use of the formula below or creating a right triangle out of the two points.

Using the formula √[(–2 – 1)² + (4 – 1)²] is √[9 + 9] which equals √18.

Although we don't know the square root of 18 automatically, we know that it will fall between √16 and √25 or 4 and 5.  Since Quantity A is 4 and Quantity B has to be between 4 and 5, Quantity B is greater.

distance² = (x₂ – x₁)² + (y₂ – y₁)²

Looking at the two order pairs given, x₁ = 1, y₁ = 1, x₂ = 7, y₂ = 9. 

distance² = (7 – 1)² + (9 – 1)² = 6² + 8² = 100

distance = 10

distance² = (x₂ – x₁)² + (y₂ – y₁)² + (z₂ – z₁)²

              = (4 – 2)² + (6 – 3)² + (5 – 4)²

              = 2² + 3² + 1²

              = 14

distance = √14

The man travels 40 meters north, 100 meters west, and 30 meters east. After he backtracks, he now has a cumulative distance west of 70 meters and he is 40 meters north. His wife has travelled east 60 meters and south 20 meters. Their positions can be modelled by the following points:

We can use the distance fomula to find the distance between the two points.

Half of this distance would be 71.59, approximately 72 meters.

There are four shifts of the graph y = f(x):

y = f(x) + c shifts the graph c units upwards.

y = f(x) – c shifts the graph c units downwards.

y = f(x + c) shifts the graph c units to the left.

y = f(x – c) shifts the graph c units to the right.

Linear terms have only one variable in a product and no exponents other than 0 or 1. x² has an exponent other than 0 or 1 so it is not linear. yz has two variables so is also not a linear term. Linear terms cannot have functions of variables either, so sin(x) is not linear.  

We can also think of these terms somewhat like graphing equations. Linear equations are straight lines. You might recognize, for example, that x² should be a parabola. Sin(x) has a graph that looks like a harmonic wave. Clearly these two shaps aren't straight lines!

The formula for calculating slope is rise over run, or the difference in  divided by the difference in . In this case, the difference in  is 5 while the difference in  is 5, resulting in a slope of  or 1.

Slope of a line given 2 points can be found using 

.  

Therefore  

or 

The slope can be calculated from m = (y₂ – y₁)/(x₂ – x₁) = (6 – 1)/(5 + 2). Having calculated the slope, we can now use point-slope form of a line, y – y₁ = m(x – x₁), and using the second point (5, 6): y – 6 = (5/7)(x – 5). This can be rearranged into slope-intercept form to obtain: y = (5/7)x + (17/7). Because the equation is now in slope intercept form, we know that the y-intercept is 17/7.

The answer is 10.

In order to find the x-intercept we simply let all the y's equal 0