Write a linear function that represents the our savings and the savings of our friend.
Our friend, see solution.
Practice makes perfect
Consider that we are saving money to buy a bicycle that cost 175 dollars. We have 45 dollars to start and save an additional 5 dollars each week. This can be written as a linear function by calling x the number of weeks.
y=5x+45
Our friend is also saving money to buy the bicycle. We are given a graph that shows the amount y in dollars that our friend has after x weeks.
We want to know who will be the first to buy the bicycle. To do so, we will start by finding the linear function that describes the savings of our friend. Remember that functions written in slope-intercept form follow a specific format.
y= mx+ b
In this form, m is the slope and b is the y-intercept. We need to identify these values using the given points. Let's start by substituting the points (0,15) and (3,39), into the slope formula and calculating m.
We calculated that the slope is 8. Now, remember that the y-intercept is the y-value where the line crosses the y-axis. It occurs when x=0. From the graph we can see that when x=0, the value of y= 15.
The function intercepts the y-axis at (0, 15). Therefore, the value of b is 15. Now we can write a function for the line that passes through the given points.
y= 8x+ 15
We want to know the number of weeks it will take our friend to buy the bicycle. To do so, we will substitute y= 175 into the above function and solve it for x.
Our friend will have enough money to buy the bicycle in 20 weeks. Now, we will find the amount of weeks it will take us to buy the bicycle. This time we will use the function obtained for our savings.
y=5x+45
Let's substitute y= 175 into the above function and solve it for x.
