Question

Julio plans a diet to gain 0.2 kg a day. After 14 days he weighs 40 kg. Write an equation in slope intercept form to model the situation and define your variables.

Answer 1

Answer:

$y=0.2x+37.2$

Step-by-step explanation:

Julio plans to gain 0.2 kg a day, so the rate of increase of weight is 0.2 kg per day.

The slope intercept form of an equation can be written as,

$y=mx+c$

In our case, 'y' is the total weight, 'x' is the number of days, 'm' is the slope and 'c' is the initial weight.

It is found out that after 14 days he weighs 40 kg. So over 14 days Julio must have gained,

$14 \times 0.2 = 2.8 kg$ because he is gaining 0.2 kg per day after the diet plan. So initially (14 days ago) Julio weighed,

$40-2.8 = 37.2 kg$

Now, we know the slope that is rate of change and that is 0.2 kg per day. We can form the equation as,

$y = 0.2x+37.2$

As we have already defined that 'y' is the final weight, 'x' is the number of days and 'c' (37.2) is the initial weight of Julio.

So the required equation is, $y = 0.2x+37.2$.