Question

1. x: number of minutes

y: height above ground
complete the statements to show what each equation represents.
the equation y = 11x + 12 represents? after x minutes.
the equation y = 15x represents? after x minutes.

Explanation:

Step1: Analyze \( y = 11x + 12 \)

This is a linear equation in slope - intercept form \( y=mx + b \), where \( m = 11 \) (rate of change) and \( b = 12 \) (initial value). The initial height (when \( x = 0 \), i.e., at time 0 minutes) is 12 units (from the \( y \) - intercept). So this equation represents a situation where there is an initial height of 12 and then a rate of increase of 11 units per minute.

Step2: Analyze \( y=15x \)

This is a linear equation in the form \( y = mx \) (where \( b = 0 \)), so the initial height (when \( x = 0 \)) is 0, and the rate of change is 15 units per minute.

Assuming the context is about the height of an object (like a balloon or a lift) over time, the first equation (\( y = 11x+12 \)) could represent an object that starts at a height of 12 (maybe above the ground) and then rises at 11 units per minute. The second equation (\( y = 15x \)) could represent an object that starts at ground level (height 0) and rises at 15 units per minute.

If we assume the blanks are about "height" with the respective starting conditions:
For \( y = 11x + 12 \): height starting from 12 units (initial height) and increasing at 11 units per minute.
For \( y=15x \): height starting from 0 units and increasing at 15 units per minute.

(Note: Since the original problem's dropdown options are not visible, but based on the equations, we can infer the meaning. If we assume the options are related to "height with an initial height" and "height starting from ground", then:

• \( y = 11x + 12 \) represents height (with an initial height of 12) after \( x \) minutes.
• \( y = 15x \) represents height (starting from 0) after \( x \) minutes. )

Answer:

For \( y = 11x + 12 \): height (with an initial height of 12)
For \( y = 15x \): height (starting from 0)

(If there were specific options in the dropdown, we would match them. Since they are not provided, we give the general interpretation based on the linear equations.)