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 .

If the y-intercept of a line is , then the -value is  when  is zero. Write the point:

If the -intercept of a line is , then the -value is  when  is zero. Write the point:

Use the following formula for slope and the two points to determine the slope:

Use the slope intercept form and one of the points, suppose , to find the equation of the line by substituting in the values of the point and solving for , the -intercept.

Therefore, the equation of this line is .

The slope intercept form can be written as:

where  is the slope and  is the y-intercept. Plug in the values of the slope and -intercept into the equation.

The correct answer is: 

The -intercept is the value of  when the  value is equal to zero. The actual point located on the graph for an -intercept of  is . The slope, , is 2.

Write the slope-intercept equation and substitute the point and slope to solve for the -intercept:

Plug the slope and -intercept back in the slope-intercept formula:

First, find the slope of the line using the slope formula: 

.

Next we plug one of the points, and the slope, into the point-intercept line forumula:

  where m is our slope.

Then  and when we plug in point (2,3) the formula reads  then solve for b. 

.

To find the equation of the line, we plug in our m and b into the slope-intercept equation.

So,  or simplified, .

To determine the equation, first find the slope:

We want this equation in slope-intercept form, . We know  and  because we have two coordinate pairs to choose from representing an  and a . We know  because that represents the slope. We just need to solve for , and then we can write the equation.

We can choose either point and get the correct answer. Let's choose : 

multiply ""

add  to both sides

This means that the form is