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?

Question

Number of tsp, x Number of gal,y
0 0
8 5
16 10
24 15

Represent the relation using an equation. y = __ (Simplify your answer. Type an expression using x as the variable. Use integers or fractions for any numbers in the expression.)

Answer 1

To represent the relation using an equation, we can assume that the relationship is linear.

From the table, we can see that when the number of tsp is 0, the number of gal is also 0. This gives us the point (0,0).

Using the point (8,5), we can find the slope of the line:
slope = (change in y) / (change in x) = (5-0) / (8-0) = 5/8

Using the slope-intercept form of a linear equation, y = mx + b, we can plug in the slope and the coordinates of one point (0,0) to find the y-intercept (b).

0 = (5/8)(0) + b
0 = 0 + b
b = 0

So the equation representing the relation between the teaspoons of powder used and the gallons of fertilizer made is: y = (5/8)x