This problem may seem slightly confusing with how the information is given. It's important to pay attention to what is being asked of us: to find the equation of a line. 

All we're provided with is the y-intercept and the slope of the line. This is enough information. Normally the point-slope formula is used when in need of finding the equation of a line, but we don't have enough information for that route. In this problem it's helpful to remember the general skeleton of a linear equation:

, where  is the slope and  is the y-intercept.

Merely substituting in the provided information will yield us the answer.

 because the slope is  and the y-int is .

This kind of a problem can be easily solved for by using the point-slope formula because they've provided us with a slope and a point (coordinate). 

 where  is slope and  and  refer to the point provided. 

With the point-slope formula, the equation of the line may be simply solved for via substituting in the known information. The resulting answer will be in the  form. 

The only information provided in this problem is the two points the specified line passes through. Although it may seem like not enough information, but this is enough to solve for the equation of the line through the point-slope formula:

 where  is slope and  and  refers to either one of the given points.

We can see that we have fulfilled the requirement for a point, but are still missing the slope. The slope can be attained using the two given points.

The slope of a line is a measure of the rate of change of the incline of a line. Slope is more commonly taught as "rise over run", and may be solved for by using the following formula: 

, where m denotes slope. Rise denotes change in the y-axis where run denotes change in the x-axis. This makes sense because rise indicates a vertical change while run indicates a horizontal change. 

Upon arbitrarily assigning the points as  and , we can substitute the given information and solve for slope. 

Now we have both requirements for the point-slope formula and can solve for the equation of the line. 

To solve this problem, first we need to find the slope of the line between two points using the following formula:

Plug in (x1,y1)=(-2,-2) and (x2,y2)=(2,-4):

Next we need to remember point-slope formula:

Then we plug in m=-1/2 and (x1,y1)=(-2,-2) and solve:

To solve this problem, first we need to find the slope of the line between two points using the following formula:

Plug in (x2,y2)=(3,2) and (x1,y1)=(1,1):

Next we need to remember point-slope formula:

Then we plug in m=1/2 and (x2,y2)=(3,2) and solve:

To solve this problem, first we need to find the slope of the line between two points using the following formula:

Plug in (x2,y2)=(4,2) and (x1,y1)=(-2,1):

Next we need to remember point-slope formula:

Then we plug in m=1/6 and (x2,y2)=(4,2) and solve:

To solve this problem, first we need to find the slope of the line between two points using the following formula:

Plug in (x1,y1)=(3,-1) and (x2,y2)=(1,2):

Next we need to remember point-slope formula:

Then we plug in m=-3/2 and (x2,y2)=(1,2) and solve:

First, determine the number of cups of coffee with which Kim starts. The question says that Kim begins with three times more coffee than Ryan's initial four cups. Therefore, Kim begins with: 

 cups of coffee.

Next, determine the rate at which Kim drinks coffee. The question states that Kim drinks coffee half as fast as Ryan, who drinks the coffee at a rate of  cups per minute. Therefore, Kim drinks coffee at a rate of 

 cups per minute.

Now, realize that the initial amount of coffee represents the y-intercept (or c-intercept in this problem) as it is the y-value (c-value) when x=0 (m=0). Next, realize that the rate of Kim's coffee drinking is the slope of the equation.

In this instance, however, the coffee is disappearing as she drinks it, so the slope must be negative. Finally, put all of this information together using the slope-intercept form of a line to get: 

.

At first glance, it may seem that there is not enough information to determine the equation for either line. Notice, however, that the blue line passes through the origin, so we therefore know two points which lie on the blue line. These points are (0,0) and (2,4). Let's use these points to determine the slope of the blue line as such: .

Now, we may use this slope, to determine the slope of the perpendicular, red line. The slope of the red line is the negative reciprocal of the slope of the blue line because they are normal to one another. Therefore, the slope of the red line is 

.

Additionally, we are given a point through which the red line passes. This point is (0,3). We may immediately identify that this point represents the y-intercept, and so the y-intercept of the red line is . 

Let's now use the information about the red line to write the equation of that line in slope-intercept form as: 

.

When finding the equation of a line given two points, we must first find the slope of the line.  To find the slope of a line in slope-intercept form

where m is the slope, we calculate

where  and  are the points.  Given the points, we can substitue. We get

Now that we know the slope, we can substitute the slope into the slope-intercept form

All we need to do now if find the value of b.  To do that, we will substitute one of the points into the equation.  Let's use (4, 5).  So,

So if we substitute the value of b into the slope-intercept form with the slope included, we get

which can also be written as