Geometry - How to find out if a point is on a line with an equation

Which of the following points is found on the line ?

Explanation

To find which point is on the line, take the -coordinate, and plug it into the given equation to solve for . If the -value matches the -coordinate of the same point, then the point is on the line.

Plugging in into the given equation will give the following:

Thus, is on the line.

Which of the following points exist on the line ?

Explanation

The line is a vertical line. This means that any point with an -value of will exist on the line.

The only possible point with an -value of is .

True or false:

The lines of the equations

and

intersect at the point .

(Note: You are given that the lines are distinct)

False

True

Explanation

If two distinct lines intersect at the point - that is, if both pass through this point - it follows that is a solution of the equations of both. Therefore, set in the equations and determine whether they are true or not.

Examine the second equation:

False; is not on the line of this equation.

Therefore, the lines cannot intersect at .

Which of the following points is found on the line $y=\frac{1}{6}x+5$ ?

Explanation

To find which point is on the line, take the -coordinate, and plug it into the given equation to solve for . If the -value matches the -coordinate of the same point, then the point is on the line.

Plugging in into the given equation will give the following:

$y=\frac{1}{6}x+5$

$y=\frac{1}{6}(24)+5=4+5=9$

Thus, is on the line.

Which of the following points does NOT lie on the graph of

Explanation

To find if a point lies on a graph or not, simply plug the x and y values into your equation and see if it holds true. Plugging our x values into the equation gives us the following:

and

So our points are and . This makes the only point that does not lie on our graph.

Which of the following points is found on the line ?

Explanation

To find which point is on the line, take the -coordinate, and plug it into the given equation to solve for . If the -value matches the -coordinate of the same point, then the point is on the line.

Plugging in into the given equation will give the following:

Thus, is on the line.

Which point will exist on the line ?

Explanation

The line is a horizontal line with points all -values equal to .

The only possible answer with a -value of is .

Which of the following points is found on the line ?

Explanation

To find which point is on the line, take the -coordinate, and plug it into the given equation to solve for . If the -value matches the -coordinate of the same point, then the point is on the line.

Plugging in into the given equation will give the following:

Thus, is on the line.

Which point is on the line ?

$(-\frac{1}{2}, 5)$

$(\frac{1}{2}, -3 )$

Explanation

A point is on a line if, plugged in, it creates a true mathematical equation.

For example, is definitely on the line because when you plug it in, it creates a true equation:

plug in the and values

multiply

this is true, so that point is on the line

The point that does not work is $(-\frac{1}{2}, 5)$ :

$5 = 2(-\frac{1}{2 }) -4$ multiply

subtract

Since this is not true, the point is NOT on the line.

Which of the following points is found on the line $y=-\frac{3}{2}x+10$ ?

Explanation

To find which point is on the line, take the -coordinate, and plug it into the given equation to solve for . If the -value matches the -coordinate of the same point, then the point is on the line.