First, use the given points to calculate the slope. Then, identify the y-intercept.
See solution.
Practice makes perfect
We are given a table that shows the amounts y in tons of waste left in a landfill after x months of waste relocation.
x
0
6
12
y
15
12
9
Equations 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 (0,15) and (6,12), into the slope formula and calculating m.
We calculated that the slope of the given equation is - 0.5, which means that the waste decrease by 0.5 tons each month. Now, remember that 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= 15.
x
0
6
12
y
15
12
9
The function intercepts the y-axis at (0, 15), which means that there are 15 tons of waste in the beginning of the relocation project. Therefore, the value of b is 15. Now that we have the slope and the y-intercept, we can write a equation for the line that passes through the given points.
y= - 0.5x+ 15
We want to find the number of months it will take to empty the landfill. Since the y-values represent the amount of waste in the landfill, an empty landfill corresponds to y=0. Let's substitute this into our equation and solve for x.
