Question

jalen is rock climbing. he starts at 12 feet above sea level. he climbs at a constant rate. after 11 minutes, he is at 21.68 feet. which equation shows how jalens height, y, depends on the number of minutes, x, it takes him to climb? (1 point) \\(\circ\\ y = 1.97x\\) \\(\circ\\ y = 3.06x + 12\\) \\(\circ\\ y = 0.88x + 12\\) \\(\circ\\ y = -0.88x + 12\\) graphing calculator

Explanation:

Step1: Determine the slope formula

The general form of a linear equation is \( y = mx + b \), where \( m \) is the slope (rate of change) and \( b \) is the y - intercept (initial value). Here, the initial height (when \( x = 0 \), at time 0 minutes) is 12 feet, so \( b=12 \). To find the slope \( m \), we use the formula \( m=\frac{y_2 - y_1}{x_2 - x_1} \). We know that when \( x_1 = 0 \), \( y_1=12 \) (starting point) and when \( x_2 = 11 \), \( y_2 = 21.68 \).

Step2: Calculate the slope

Substitute the values into the slope formula: \( m=\frac{21.68 - 12}{11-0}=\frac{9.68}{11}=0.88 \).

Step3: Form the equation

Since \( m = 0.88 \) and \( b = 12 \), the equation of the line is \( y=0.88x + 12 \).

Answer:

\( y = 0.88x + 12 \) (the option: \( y = 0.88x + 12 \))