Using the table, we will have five ordered pairs. Plotting these points, we can have the graph.
Interpretation of the Table: See solution. Equation: y=-50x+62250 Graph:
Practice makes perfect
The given table shows the relationship between the number of sprays x a bottle of throat spray delivers and the amount of spray y (in milligrams) left in the bottle.
Throat Spray
Numbers of Sprays, x
0
1
2
3
4
Spray Left (mg), y
62 250
62 200
62 150
62 100
62 050
Let's interpret this table!
Interpretation of the Table
When we examine the rate of change of the variables, we see that the amount of spray decreases by 50 as the number of sprays increases by 1. We can use this to write an equation that represents the amount of spray left in the bottle.
Equation
Using the table and our interpretation of it, we can write an equation.
y= -50x
Does the formula work? Let's check it for 0 spray!
As we can see, the formula does not work for 0 spray. Let's apply the formula to the other figures and try to figure out the missing piece.
Number of Sprays x
y=-50x
Amount Found by the Formula
Actual Amount
0
y=-50( 0)
0
62 250
1
y=-50( 1)
-50
62 200
2
y=-50( 2)
-100
62 150
3
y=-50( 3)
-150
62 100
4
y=-50( 4)
-200
62 050
The amount found by the incomplete formula is always 62 250 less than the actual amount. Thus, we can complete our formula by adding 62 250 to the formula.
y= -50x+62 250
Next, we will make a graph that represents the amount of the spray depending on the number of sprays.
Graph
Using the table, we have five ordered pairs.
(0,62 250) (1,62 200) (2,62 150)
(3,62 100) (4,62 050)
By plotting these points on the coordinate plane, we get our graph.
