Solved on Jan 11, 2024

Find the linear equation $y = mx + b$ describing a baby's weight, where the baby weighs 7 lbs at birth and gains 5 lbs every 2 months.

STEP 1

Assumptions
1. The initial weight of the baby at birth is 7 pounds.
2. The baby gains 5 pounds every 2 months.
3. The variable $x$ represents the age of the baby in months.
4. The variable $y$ represents the weight of the baby in pounds.
5. We are looking for a linear equation of the form $y = mx + b$ .

STEP 2

Determine the slope ( $m$ ) of the line, which represents the rate of weight gain per month.
$m = \frac{\text{Weight gain over period}}{\text{Time period in months}}$

STEP 3

Calculate the slope using the given weight gain and time period.
$m = \frac{5 \text{ pounds}}{2 \text{ months}}$

STEP 4

Simplify the slope to get the weight gain per month.
$m = \frac{5}{2} \text{ pounds per month}$

STEP 5

Identify the y-intercept ( $b$ ) of the line, which represents the initial weight of the baby at birth (when $x = 0$ ).
$b = 7 \text{ pounds}$

STEP 6

Write the equation of the line using the slope ( $m$ ) and y-intercept ( $b$ ).
$y = mx + b$

STEP 7

Substitute the values of $m$ and $b$ into the equation.
$y = \frac{5}{2}x + 7$
The equation that describes the baby's weight as a function of age in months is: $y = \frac{5}{2}x + 7$

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Find the linear equation $y = mx + b$ describing a baby's weight, where the baby weighs 7 lbs at birth and gains 5 lbs every 2 months.

STEP 1

STEP 2

Determine the slope ( $m$ ) of the line, which represents the rate of weight gain per month.
$m = \frac{\text{Weight gain over period}}{\text{Time period in months}}$

STEP 3

Calculate the slope using the given weight gain and time period.
$m = \frac{5 \text{ pounds}}{2 \text{ months}}$

STEP 4

Simplify the slope to get the weight gain per month.
$m = \frac{5}{2} \text{ pounds per month}$

STEP 5

Identify the y-intercept ( $b$ ) of the line, which represents the initial weight of the baby at birth (when $x = 0$ ).
$b = 7 \text{ pounds}$

STEP 6

Write the equation of the line using the slope ( $m$ ) and y-intercept ( $b$ ).
$y = mx + b$

STEP 7

Substitute the values of $m$ and $b$ into the equation.
$y = \frac{5}{2}x + 7$
The equation that describes the baby's weight as a function of age in months is: $y = \frac{5}{2}x + 7$

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Find the linear equation y=mx+by = mx + by=mx+b describing a baby's weight, where the baby weighs 7 lbs at birth and gains 5 lbs every 2 months.

STEP 1

STEP 2

Determine the slope (mmm) of the line, which represents the rate of weight gain per month.m=Weight gain over periodTime period in monthsm = \frac{\text{Weight gain over period}}{\text{Time period in months}}m=Time period in monthsWeight gain over period​

STEP 3

Calculate the slope using the given weight gain and time period.m=5 pounds2 monthsm = \frac{5 \text{ pounds}}{2 \text{ months}}m=2 months5 pounds​

STEP 4

Simplify the slope to get the weight gain per month.m=52 pounds per monthm = \frac{5}{2} \text{ pounds per month}m=25​ pounds per month

STEP 5

Identify the y-intercept (bbb) of the line, which represents the initial weight of the baby at birth (when x=0x = 0x=0).b=7 poundsb = 7 \text{ pounds}b=7 pounds

STEP 6

Write the equation of the line using the slope (mmm) and y-intercept (bbb).y=mx+by = mx + by=mx+b

STEP 7

Substitute the values of mmm and bbb into the equation.y=52x+7y = \frac{5}{2}x + 7y=25​x+7The equation that describes the baby's weight as a function of age in months is: y=52x+7y = \frac{5}{2}x + 7y=25​x+7

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find the linear equation $y = mx + b$ describing a baby's weight, where the baby weighs 7 lbs at birth and gains 5 lbs every 2 months.

Determine the slope ( $m$ ) of the line, which represents the rate of weight gain per month.
$m = \frac{\text{Weight gain over period}}{\text{Time period in months}}$

Calculate the slope using the given weight gain and time period.
$m = \frac{5 \text{ pounds}}{2 \text{ months}}$

Simplify the slope to get the weight gain per month.
$m = \frac{5}{2} \text{ pounds per month}$

Identify the y-intercept ( $b$ ) of the line, which represents the initial weight of the baby at birth (when $x = 0$ ).
$b = 7 \text{ pounds}$

Write the equation of the line using the slope ( $m$ ) and y-intercept ( $b$ ).
$y = mx + b$

Substitute the values of $m$ and $b$ into the equation.
$y = \frac{5}{2}x + 7$
The equation that describes the baby's weight as a function of age in months is: $y = \frac{5}{2}x + 7$