You can make 5 gal of liquid fertilizer by mixing 8 tsp of powdered fertilizer with water. Represent the relation between the teaspoons of powder used and the gallons of fertilizer made using a table, an equation, and a graph is the amount of fertilizer made a function of the amount of powder used?
Number of tsp, x Number of gal,y
0 0
8 5
16 10
24 15
Represent the relation using an equation. y = (5/8)x (Simplify your answer. Type an expression using x as the variable. Use integers or fractions for any numbers in the expression.)
Which graph below represents the relation?
The correct equation for the relation between the teaspoons of powder used and the gallons of fertilizer made is y = (5/8)x. This equation represents a proportional relationship, where the amount of fertilizer made (y) is directly proportional to the amount of powder used (x), with a constant ratio of 5/8.
Among the given graphs, the correct one that represents this proportional relationship is a straight line passing through the origin (0,0) and having a positive slope.
To represent the relation between the teaspoons of powder used and the gallons of fertilizer made, we can create a table, an equation, and a graph.
Table:
Number of tsp, x | Number of gal, y
----------------|-----------------
0 | 0
8 | 5
16 | 10
24 | 15
Equation:
To find the equation that represents the relation, we can analyze the pattern in the table. As the number of teaspoons increases by 8, the number of gallons increases by 5. So, we can deduce that for every 8 teaspoons, there is an increase of 5 gallons.
Therefore, we can write the equation as:
y = (5/8)x
Graph:
Based on the equation y = (5/8)x, we can plot the points from the table on a graph.
The x-axis represents the number of tsp (teaspoons) of powder used, and the y-axis represents the number of gallons of fertilizer made.
On the graph, plot the points (0,0), (8,5), (16,10), and (24,15).
Now draw a line connecting these points.
The correct graph is the one that shows a straight line passing through these points.
The relation between the teaspoons of powder used and the gallons of fertilizer made can be represented using a table, an equation, and a graph.
Table:
Number of tsp (x) | Number of gal (y)
0 | 0
8 | 5
16 | 10
24 | 15
Equation: y = (5/8)x
In this equation, y represents the number of gallons of fertilizer made, and x represents the number of teaspoons of powder used.
Graph:
The graph that represents the relation is a straight line that passes through the points (0,0), (8,5), (16,10), and (24,15). The line will have a positive slope, since as the number of teaspoons of powder increases, the number of gallons of fertilizer made also increases.