Learn about Applications of Lines in a Plane In this lesson, let’s learn how we apply lines and slopes of lines in a plane in real life situations. So it says Ceciles is trying to decide between two health clubs or sports club plans. Plan A says $140 upfront enrollment fee and $25 a month after that. Plan says $60 upfront enrollment and $45 a month after that. So let’s say X is the number of months and Y is total dollars spent. We need to find out after how many months would both plans’ total costs be same? So this is equation one, Y is the total dollar spent, Y is the total dollar spent which would be in case of plan A is $140 plus $25 times X numbers of months. Equation two is Y would be $60 upfront plus $45 times X, $60 upfront and then $45 each month. So let’s do this, when x and y—let’s find the few coordinates. If x is zero and y is one, what do I get? When x is zero y is 140, when x is one 140 plus 25 is 165 that’s the first equation. In case of second equation, what do I get? If X is zero, this is 60 and if x is one it’s 105. All I did was x is one, 45 times one is 45 plus 60 Y is 105. So I’ve got the coordinates of two points or each of the two equations. Let’s actually plot them. So line one, when x is zero, y is 140 that’s here. Line two, when x is zero y is 60. Then, when x is one for line one, y is 165, when x is one for line two y is 105 so we plotted both these points and then I’m just going to draw a line through them. Now, the point the two lines intersect which is 240 and four is the place where the plans become equal. So after four months the total of costs for both plans equals 240. This is the intersection of both. Let’s double check if this is the answer. After four months for plan A, what do I get? Four months I spent $140 upfront plus $25 times four equals $240, that’s correct. For equation two, plan B, I spent $60 upfront plus $45 times four which is $180 plus $60 is $240 again the same. So after four months both plan A and B are equal that’s the answer.