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Olivia is growing roses and keeps track of how much fertilizer (in ounces) she adds to the soil and how many blooms each rose bush has. She finds a linear relationship that can be modeled by the equation [tex]$y = 1.345x + 4$[/tex]. When will Olivia only have 4 blooms?

A. When she adds no fertilizer.
B. Every bush will only have 4 blooms.
C. When she only adds 1 ounce of fertilizer.
D. It is not possible for her to only have 4 blooms.



Answer :

GinnyAnswer
To determine when Olivia will have exactly 4 blooms on her rose bushes, we start by analyzing the given linear relationship modeled by the equation:

[tex]\[ y = 1.345x + 4 \][/tex]

where:
- [tex]\( y \)[/tex] represents the number of blooms,
- [tex]\( x \)[/tex] represents the amount of fertilizer (in ounces).

We are asked to find the value of [tex]\( x \)[/tex] that results in [tex]\( y \)[/tex] equaling 4 blooms. Therefore, we set [tex]\( y = 4 \)[/tex] in the equation and solve for [tex]\( x \)[/tex]:

[tex]\[ 4 = 1.345x + 4 \][/tex]

Next, we isolate the term involving [tex]\( x \)[/tex]. Start by subtracting 4 from both sides of the equation:

[tex]\[ 4 - 4 = 1.345x + 4 - 4 \][/tex]

This simplifies to:

[tex]\[ 0 = 1.345x \][/tex]

Next, solve for [tex]\( x \)[/tex] by dividing both sides of the equation by 1.345:

[tex]\[ \frac{0}{1.345} = \frac{1.345x}{1.345} \][/tex]

This simplifies to:

[tex]\[ 0 = x \][/tex]

Thus, [tex]\( x = 0 \)[/tex].

The result shows that Olivia will have exactly 4 blooms when she adds no fertilizer (0 ounces). Hence, the correct answer is:

A) When she adds no fertilizer.