To find the length between two points, we use the following distance formula:

where  and  are the points given.

Using the given points

 and 

we can substitute into the formula.  We get

Therefore, the distance between the points  and  is .

Use the distance formula to determine the distance of this line.

Substitute the points into the equation.

Simplify the radical.

Pull out the common factors.  This radical can still be reduced.

The exact length of the line is:  

The distance formula is:

Plug in these points into the distance formula.

Reduce:

The distance formula is:

Plug in Seven and Joel's coordinates into this formula.

Write the distance formula.

Substitute the given points into the formula.

Simplify the terms inside the parentheses.

The answer is: 

To find out if a point (x, y) is on the graph of a line, we plug in the values and see if we get a true statement, such as 10 = 10. If we get something different, like 6 = 4, we know that the point is not on the line because it does not satisfy the equation. In the given choices, when we plug in (1, 10) we get 10 = 7 + 2, which is false, making this is the desired answer.

y = 7x + 2

(2, 16) gives 16 = 7(2) + 2 = 14 + 2 = 16

(–1, –5) gives –5 = 7(–1) + 2 = –7 + 2 = –5

(0, 2) gives 2 = 7(0) + 2 = 0 + 2 = 2

(–2, –12) gives –12 = 7(–2) + 2 = –14 + 2 = –12

All of these are true.

(1, 10) gives 10 = 7(1) + 2 = 7 + 2 = 9

10 = 9 is a false statement.

To determine whether a point is on a line, simply plug the points back into the equation. When we plug in (2,7) into the equation of  as  and  respectively, the equation works out, which indicates that the point is located on the line.

Lines that have the same slope are parallel (unless the two lines are identical) and lines with slopes that are opposite-reciprocals are perpendicular. So, the only statements left to evaluate are the two that contain a set of points.

Consider  and .

So the slope, or , is 2.

Plugging the point  into the half-finished equation  gives us a  value of . So that statement is true and the only one that could be the answer is the statement containing  and .

Let's check it just in case.

  gives us a slope value of 6, so we can already tell the equation for the line will not be . We have found our answer.

To find out if a point is on a line, you can plug the points back into an equation. If the values equal one another, then the point must be on a line. In this case, the only equation where (6,5) would correctly fit as an  value is .

The easiest way to find out if a point falls on a specific line is to plug the first value of the point in for  and the second value for .

If we do this for , we find that

which is true.

The equation also holds true for , but is false for the other values. So, two of the answer choices are correct.