In finding the equation of the line given its slope and a point through which it passes, we can use the slope-intercept form of the equation of a line:

, where  is the slope of the line and  is its -intercept.

Since the problem gives us the slope of the line , we just need to use the point that is given to us to find the -intercept. Plug in known values for  and  taken from the given point into the  equation and solve for  to find the -intercept:

Multiply:

Subtract  from both sides of the equation:

Now, we can write the final equation by plugging in the given slope  and the -intercept :

The question gives us both the slope and the -intercept of the line, allowing us to write the following equation by inserting those values into the slope-intercept form of the equation of a line, :

Alternatively, if you did not realize that the problem gives you the -intercept, you could solve it by using the slope-intercept form of the equation of a line. Since the problem gives us the slope of the line , we would just need to use the point that is given to us to find the -intercept. We could plug in the known values for  and  taken from the given point into the  equation and solve for  to find the -intercept:

Multiplying leaves us with:

We could then substitute in the given slope and the -intercept into the  equation to arrive at the correct answer:

The question gives us both the slope and the -intercept of the line. Remember that  represents the slope, and  represents the -intercept to write the following equation:

Alternatively, if you did not realize that the problem gives you the -intercept, you could solve it by using the slope-intercept form of the equation of a line:

, where  is the slope of the line and  is its -intercept.

Since the problem gives us the slope of the line , we would just need to use the point that is given to us to find the -intercept. We could plug in the known values for  and  taken from the given point into the  equation and solve for  to find the -intercept:

Multiplying leaves us with:

.

We could then substitute in the given slope and the -intercept into the  equation to arrive at the correct answer:

First, notice that our -intercept for this line is ; we can tell this because one of the points, , is on the -axis since it has a value of  for . 

Now, we need to find the slope of the line. We can do that by using the slope equation:

We can substitute in the values of the provided points—,,  and —and then solve for the slope of the line that connects them:

Now, put the two pieces of information together and substitute them into the  equation to solve the problem:

First, notice that our -intercept for this line is ; we can tell this because one of the points, , is on the -axis since it has a value of  for . 

Now, we need to find the slope of the line. We can do that by using the slope equation:

We can substitute in the values of the provided points—,,  and —and then solve for the slope of the line that connects them:

Now, put the two pieces of information together and substitute them into the  equation to solve the problem:

First, notice that our -intercept for this line is ; we can tell this because one of the points, , is on the -axis since it has a value of  for . 

Now, we need to find the slope of the line. We can do that by using the slope equation:

We can substitute in the values of the provided points—,,  and —and then solve for the slope of the line that connects them:

Now, put the two pieces of information together and substitute them into the  equation to solve the problem:

First, we need to find the slope of the line. We can do that by using the slope equation:

We can substitute in the values of the provided points—,,  and —and then solve for the slope of the line that connects them:

Next, plug one of the points' coordinates and the slope to the  equation and solve for  to find the -intercept. For this example, let's use the point :

Multiply:

Change  from a whole number to a mixed number with  in the denominator, just like in the fraction :

Subtract  from each side of the equation:

Finally, put the slope and the -intercept into the  equation to arrive at the correct answer:

First, notice that our -intercept for this line is ; we can tell this because one of the points, , is on the -axis since it has a value of  for . 

Now, we need to find the slope of the line. We can do that by using the slope equation:

We can substitute in the values of the provided points—,,  and —and then solve for the slope of the line that connects them:

Now, put the two pieces of information together and substitute them into the  equation to solve the problem:

The slope of a line is equal to . 

Given that the box is one foot tall, the rise will be equal to "1."

Given that the board is four feet long, the run will be equal to "4."

Therefore, the slope is equal to .

To find the slope, put the equation in  form.

Since , that must be the slope of the line.