Question

elijah started hiking at an elevation of -12 feet below sea level. he hiked up at a rate of 9 feet per minute. this graph represents the relationship between the number of minutes and his elevation. use the slope and vertical intercept to write an equation. slope = 9 vertical intercept = -12 elevation = starting elevation + change in elevation from hiking

Explanation:

Step1: Recall the slope - intercept form

The slope - intercept form of a linear equation is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept (vertical intercept). In the context of this problem, let $y$ represent the elevation (in feet) and $x$ represent the number of minutes. The slope $m = 9$ (the rate of hiking in feet per minute) and the vertical intercept $b=- 12$ (the starting elevation).

Step2: Identify the components

• The "elevation" is the dependent variable (equivalent to $y$ in the slope - intercept form).
• The "starting elevation" is the vertical intercept, which is - 12.
• The "change in elevation from hiking" is the product of the slope (rate) and the number of minutes $x$, so it is $9x$ (since the rate is 9 feet per minute, after $x$ minutes, the change in elevation is $9\times x$).

Step3: Write the equation

Using the relationship: elevation = starting elevation+change in elevation from hiking, we substitute the values. The starting elevation is - 12 and the change in elevation from hiking is $9x$. So the equation is $y=-12 + 9x$ (or $elevation=-12 + 9x$). In the given boxed form:

• The first box (elevation) can be represented as a variable, say $y$ (or elevation), the second box (starting elevation) is - 12, and the third box (change in elevation from hiking) is $9x$. But if we follow the structure in the problem:

elevation $=-12 + 9x$

Answer:

elevation $=-12 + 9x$ (or in the boxed form as per the problem's structure: first box: elevation, second box: - 12, third box: $9x$)