Start by rewriting the equation into slope-intercept form.

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.

Start by rewriting the equation into slope-intercept form.

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.

Start by rewriting the equation into slope-intercept form.

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.

Start by rewriting the equation into slope-intercept form.

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.

Start by rewriting the equation into slope-intercept form.

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.

A line of an equation passes through the point with coordinates if and only if, when , the equation is true. Substitute for and :

- this is false.

The line does not pass through the point.

The coordinates of the origin are , so the line of an equation passes through this point of and only if is a solution of the equation - or, equivalently, if and only if setting and makes the equation a true statement. Substitute both values:

The statement is true, so the line does pass through the origin.

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 .

If we have two points, we can find the slope of the line between them by using the definition of the slope:

    where the triangle is the greek letter 'Delta', and is used as a symbol for 'difference' or 'change in'

Now that we have our slope ( , simplified to ), we can write the equation for slope-intercept form:

   where  is the slope and  is the y-intercept

In order to find the y-intercept, we simply plug in one of the points on our line

So our equation looks like   

Because we have the desired slope and the y-intercept, we can easily write this as an equation in slope-intercept form (y=mx+b).

This gives us . Because this does not match either of the answers in this form (y=mx+b), we must solve the equation for x. Adding 5 to each side gives us . We can then multiple both sides by 3 and divide both sides by 4, giving us .