Question

at a science museum, a conveyor belt is behind a coordinate plane that is drawn on a plexiglass sheet. the conveyor belt lifts and carries a ball in a northeastern direction, upward one cm and to the right 5 cm. at the top, the ball is at the point (-4, 20). which form of linear equation would take the least number of steps to write in order to model this scenario, and what is the equation? let x represent the number of cm to the right, and y represent the number of cm up.

• slope intercept form: y = (1/5)x + 104/5
• point slope form: y - 20 = (1/5)(x + 4)
• point slope form: y - 20 = (1/5)(x - 4)
• standard form: x - 5y = -104

question 4
2 points
the temperature of a glass of water was measured at 72°f and then put into a freezer. every minute after that it was 2°f colder. which form of linear equation would be best to model this situation, and what is the equation? let x represent the number of minutes that pass, and y represent the temperature of the water, in °f.

• standard form: -2x + y = 72
• slope intercept form: y = 2x + 72
• slope intercept form: y = -2x + 72
• standard form: 2x + y = 72

Explanation:

First Problem (Conveyor Belt)

Step1: Calculate slope

Slope $m = \frac{\text{rise}}{\text{run}} = \frac{1}{5}$

Step2: Identify given point

Point: $(-4, 20)$

Step3: Apply point-slope formula

Point-slope formula: $y - y_1 = m(x - x_1)$
Substitute values: $y - 20 = \frac{1}{5}(x - (-4)) = \frac{1}{5}(x + 4)$

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Second Problem (Freezer Water Temperature)

Step1: Define slope and intercept

Slope $m = -2$ (temperature drops 2°F/min), y-intercept $b = 72$ (initial temp)

Step2: Apply slope-intercept formula

Slope-intercept formula: $y = mx + b$
Substitute values: $y = -2x + 72$

Answer:

Point slope form: $y - 20 = \frac{1}{5}(x + 4)$