First, use the given points to calculate the slope.
Then, identify the y-intercept.
We will run out of data first.
Practice makes perfect
Consider that we use 0.08 gigabytes of data each month. We are given a table that shows the amount y in gigabytes of data that our friend has left x days after the start of each month.
Day, x
Data (gigabytes), y
0
3
7
2.3
14
1.6
We want to know who runs out of data first if we start each month with 2 gigabytes of data. Since y represents the data left, our friend will be out of data when y=0. To calculate it, let's write a function that describes this situation. Remember that functions written in slope-intercept form follow a specific format.
y= mx+ bIn this form, m is the slope and b is the y-intercept. We need to identify these values using the given table. Let's start by substituting the points (0,3) and (7,2.3), into the slope formula and calculating m.
We calculated that the slope is - 0.1, which means that each month the data of our friend decrease by 0.1 gigabytes. The y-intercept is the y-value where the line crosses the y-axis. It occurs when x=0. From the table we can see that when x=0, the value of y= 3.
Day, x
Data (gigabytes), y
0
3
7
2.3
14
1.6
The function intercepts the y-axis at (0, 3), which means that our friend start with 3 gigabytes of data each month. Therefore, the value of b is 3. We can write the function for the line that passes through the given points.
y= - 0.1x+ 3
Now that we have the function that represents the amount of data that our friend left, we can predict after how many days our friend will runs out of data by substituting y=0 into the obtained equation and solve it for x.
Our friend will run out of data in 30 days. Now, we can write a function that describes our data usage. To do so, consider that our amount of data will be equal to the difference between 2 gigabytes and the product of 0.08 multiplied by the number x of days.
y= 2-0.08x
Again, we need to calculate when we will run out of data. It will occurs when y=0. Let's substitute y=0 into the above equation and solve it for x.
