Math / Algebra

QuestionWRITE AN EQUATION TO REDRESENT STEVE THE SHARK'S SEA LEVEL IN SLOPE-INTERCEPT FORM. Steve the shark is currently 300 feet below sea level and is descending at a rate of 50 feet per minute

Studdy Solution

STEP 1

What is this asking? We need to write an equation that shows Steve's depth below sea level over time, using the slope-intercept form. Watch out! Descending means going deeper, so the rate is negative!
Don't forget that slope-intercept form is $y = mx + b$ , where $m$ is the slope (rate of change) and $b$ is the y-intercept (initial value).

STEP 2

1. Define the variables and identify the slope and y-intercept.
2. Write the equation in slope-intercept form.

STEP 3

Let $y$ represent Steve's depth below sea level (in feet) and $x$ represent the time (in minutes).
We're doing this so we can connect our equation to the real-world situation!

STEP 4

Steve starts at 300 feet below sea level.
This is our initial value, so $b = -300$ .
Remember, below sea level means negative depth!

STEP 5

Steve is descending at a rate of 50 feet per minute.
Since he's going down, this rate is negative.
So, our rate of change, or slope, is $m = -50$ .

STEP 6

We know that slope-intercept form is $y = mx + b$ .
We've found that $m = -50$ and $b = -300$ .
Let's plug these values into the equation!

STEP 7

Substituting our values, we get $y = -50x + (-300)$ , which simplifies to $y = -50x - 300$ .
This equation tells us Steve's depth ( $y$ ) at any given time ( $x$ )!

STEP 8

The equation representing Steve the Shark's sea level in slope-intercept form is $y = -50x - 300$ .

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QuestionWRITE AN EQUATION TO REDRESENT STEVE THE SHARK'S SEA LEVEL IN SLOPE-INTERCEPT FORM. Steve the shark is currently 300 feet below sea level and is descending at a rate of 50 feet per minute

Studdy Solution

STEP 1

STEP 2

1. Define the variables and identify the slope and y-intercept.
2. Write the equation in slope-intercept form.

STEP 3

Let $y$ represent Steve's depth below sea level (in feet) and $x$ represent the time (in minutes).
We're doing this so we can connect our equation to the real-world situation!

STEP 4

Steve starts at 300 feet below sea level.
This is our initial value, so $b = -300$ .
Remember, below sea level means negative depth!

STEP 5

Steve is descending at a rate of 50 feet per minute.
Since he's going down, this rate is negative.
So, our rate of change, or slope, is $m = -50$ .

STEP 6

We know that slope-intercept form is $y = mx + b$ .
We've found that $m = -50$ and $b = -300$ .
Let's plug these values into the equation!

STEP 7

Substituting our values, we get $y = -50x + (-300)$ , which simplifies to $y = -50x - 300$ .
This equation tells us Steve's depth ( $y$ ) at any given time ( $x$ )!

STEP 8

The equation representing Steve the Shark's sea level in slope-intercept form is $y = -50x - 300$ .

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QuestionWRITE AN EQUATION TO REDRESENT STEVE THE SHARK'S SEA LEVEL IN SLOPE-INTERCEPT FORM. Steve the shark is currently 300 feet below sea level and is descending at a rate of 50 feet per minute

Studdy Solution

STEP 1

STEP 2

1. Define the variables and identify the slope and y-intercept.2. Write the equation in slope-intercept form.

STEP 3

Let yyy represent Steve's depth below sea level (in feet) and xxx represent the time (in minutes).We're doing this so we can connect our equation to the real-world situation!

STEP 4

Steve *starts* at 300 feet *below* sea level.This is our **initial value**, so b=−300b = -300b=−300.Remember, below sea level means negative depth!

STEP 5

Steve is descending at a rate of 50 feet per minute.Since he's going *down*, this rate is *negative*.So, our **rate of change**, or slope, is m=−50m = -50m=−50.

STEP 6

We know that slope-intercept form is y=mx+by = mx + by=mx+b.We've found that m=−50m = -50m=−50 and b=−300b = -300b=−300.Let's plug these values into the equation!

STEP 7

Substituting our values, we get y=−50x+(−300)y = -50x + (-300)y=−50x+(−300), which simplifies to y=−50x−300y = -50x - 300y=−50x−300.This equation tells us Steve's depth (yyy) at any given time (xxx)!

STEP 8

The equation representing Steve the Shark's sea level in slope-intercept form is y=−50x−300y = -50x - 300y=−50x−300.

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1. Define the variables and identify the slope and y-intercept.
2. Write the equation in slope-intercept form.

Let $y$ represent Steve's depth below sea level (in feet) and $x$ represent the time (in minutes).
We're doing this so we can connect our equation to the real-world situation!

Steve starts at 300 feet below sea level.
This is our initial value, so $b = -300$ .
Remember, below sea level means negative depth!

Steve is descending at a rate of 50 feet per minute.
Since he's going down, this rate is negative.
So, our rate of change, or slope, is $m = -50$ .

We know that slope-intercept form is $y = mx + b$ .
We've found that $m = -50$ and $b = -300$ .
Let's plug these values into the equation!

Substituting our values, we get $y = -50x + (-300)$ , which simplifies to $y = -50x - 300$ .
This equation tells us Steve's depth ( $y$ ) at any given time ( $x$ )!

The equation representing Steve the Shark's sea level in slope-intercept form is $y = -50x - 300$ .