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.

To determine which ordered pair satisfies the equation, it would help to rearrange the equation to slope-intercept form.

Then, plug in each ordered pair and see if it satisfies the equation. We are looking for an value that produces the desired answer.

 satisfies the equation. All of the other points do not.  

(Note: you could also use the original equation in standard form).

To determine whether a point is on a line, you can plug it into the equation to see if the equation remains valid/equal with the point.

Plugging the point (3,2) into the equation gives you

which works out. None of the other equations would remain equal after pluggin in (3,2).

To determine whether a point is located in a given line, simply plug in the coordinates of the point into the line. In this case, plugging in the coordinates into the only line where you can plug in the coordinates and have a valid equation is . Plugging in (2,7) would give you an equation of , which works out to .

To find out if a point is on a line with an equation, we just need to substitute in the point's  and  values and see if the equation holds true. For example, let's look at the point . Substitution into the equation gives us 

or 

, which is true.

So, this point does fall on the line. Doing the same with the other two points shows us that yes, all three of them fall on the line expressed by this equation.

To determine if a point is on a line you can simply subsitute the x and y coordinates into the equation. Another way to solve the problem would be to graph the line and see if it falls on the line. Plugging in  will give  which is a true statement, so it is on the line.