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

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's define the variables: let $y$ be the elevation (in feet) and $x$ be the number of minutes. The slope $m = 9$ (rate of hiking up in feet per minute) and the vertical intercept $b=- 12$ (starting elevation).

Step2: Relate to the components

The "change in elevation from hiking" is given by the slope times the number of minutes, which is $9x$ (since the rate is 9 feet per minute, after $x$ minutes, the change in elevation is $9\times x$). The "starting elevation" is - 12 feet. And the "elevation" (the final elevation) is the sum of the change in elevation from hiking and the starting elevation.

So, if we let:

• "elevation" be $y$ (the dependent variable, representing the final elevation)
• "change in elevation from hiking" be $9x$ (because rate is 9 feet per minute, so for $x$ minutes, change is $9x$)
• "starting elevation" be - 12 (the initial elevation)

Then the equation is $y=9x+( - 12)$ or $y = 9x-12$, which can be written in the form of the given boxes as: elevation $=$ change in elevation from hiking $+$ starting elevation. Substituting the values, we have elevation $=9x+( - 12)$, but in terms of the boxes: the left - most box (elevation) $=$ (change in elevation from hiking: $9x$) $+$ (starting elevation: - 12). But since we have to match with the labels:

The "elevation" is the total elevation, which is equal to the "change in elevation from hiking" (which is $9x$, since rate is 9 feet per minute, so for $x$ minutes, change is $9x$) plus the "starting elevation" (which is - 12).

Answer:

elevation $=$ change in elevation from hiking $+$ starting elevation

Filling in the values (in terms of the expressions):

The first box (elevation) should be filled with "elevation", the second box (the one after =) should be filled with "change in elevation from hiking" (which is $9x$ but in terms of the label, we use the label), and the third box should be filled with "starting elevation" (which is - 12, but in terms of the label). So the equation is:

elevation $=$ change in elevation from hiking $+$ starting elevation

If we substitute the numerical values (slope and vertical intercept) into the slope - intercept form $y=mx + b$ (where $y$ is elevation, $m = 9$, $x$ is minutes, $b=-12$), we get $y = 9x-12$, which is equivalent to elevation $=9\times$ number of minutes $+(- 12)$ (or elevation $=9x - 12$). But in terms of the given labels:

The left box (elevation) $=$ (middle box: change in elevation from hiking) $+$ (right box: starting elevation)

So the labels for the boxes are:

First box: elevation

Second box: change in elevation from hiking

Third box: starting elevation