Question

The equation 125 + 37.52x = y models the amount of money in your wallet Y is the total amount of dollars and x is the number of weeks from today.
Is the equation in slope intercept form? Explain

If you graphed this situation what would the slope represent? Explain

If you graphed this situation what would the y intercept be and what would it represent?

What units make sense for the slope?

Answer 1

The given equation is 125+37.52x=y, where y is the total amount of dollars and x is the number of weeks

This equation can be re-write as y=37.52x+125

Yes, this equation is in slope-intercept form y=mx+c having a slope, m=37.52 and the intercept, c=125.

Now, check the units,

In equation y=mx+c, units of all the three terms, i.e y, mx and c, are same.

As given that unit of y is dollar, so the unit of c is dollar and unit of $mx$ is also dollar.

As the unit of $mx$ is dollar, so the unit of m is dollar/unit of x.

As given that the unit of x is week, so the unit of m is dollar/week.

Therefore, the y-intercept, c= 125 dollars, and m=37.52 dollar/week.

The unit of the slope is dollars/week, so, the slope of the equation represents the rate of change of money in the wallet per week.

From the graph of the equation, y-intercept, c=125 dollars, is the value of y at x=0 which is the initial amount of money in the wallet.