Question

a science class is tracking the progress of plant growth. the class starts the experiment with a plant five centimeters high. the plant grows two centimeters each day. the model for plant growth y is given by: y = 2x + 5. what is the meaning of the y-intercept in this equation?

a the y-intercept is the starting date

b the y-intercept is two times larger than five

c the y-intercept is the starting height of the plant

d the y-intercept is the largest height the plant can grow

Explanation:

In the linear equation \( y = mx + b \) (where \( m \) is the slope and \( b \) is the \( y \)-intercept), the \( y \)-intercept (\( b \)) represents the value of \( y \) when \( x = 0 \). In the context of the plant growth model \( y = 2x+5 \), \( x \) represents the number of days. When \( x = 0 \) (the start of the experiment, day 0), \( y=2\times0 + 5=5 \). The initial height of the plant (at the start of the experiment) is 5 centimeters.

• Option A: The \( y \)-intercept has nothing to do with a date.
• Option B: \( 5

eq2\times5 \), so this is incorrect.

• Option D: The equation \( y = 2x + 5 \) is a linear model (assuming no upper - limit constraints from the equation itself), so it doesn't represent the largest height.

Answer:

C. the y - intercept is the starting height of the plant