Question

Kurt begins with $200 in his bank account and withdraws $10 each week.

Part A: Write an equation for the line that represents this situation in slope-intercept form

Part B: Graph the equation of the line

Answer 1

Answer: y= -10x+200

Explanation:

The y intercept is 200 as it starts off with 200. The slope would be -10 because Kurt is withdrawing money which is 10 and would be negative. Try graphing this.

Answer 2

`y=-10x+200`

Explanation:

According to the problem, Kurt is withdrawing $10 each week, but we don't how many weeks are, we just know that he is taking that amount of money constantly. So, the variable has to be "week".

On the other hand, he has $200, which is a fixed amount, it's not variable. So, this cannot be with a variable, because it shouldn't variate. Also, Kurt is constantly subtracting money from the $200, which means that the linear function has to be decreasing, and that is represent as a negative slope, which is the coefficient of the variable.

Therefore, according to all these characteristics, the line's equation or linear function should be:

`y=-10x+200`

As you can see, the negative sign represent the decreasing amount of money. The 200 represent the fixed amount of money Kurt has in the account, and the x refers to "weeks".

On the other hand, to graph the equation, we just to give specific values to the x, and see what result gives for y. This values are arbitrary, but when we want to graph a line, we just consider
`x=0` and
`y=0`, which is going to result in two different points (we just need two points to graph a line).

We build a table, to record the value of each variable:

x y

0 200

20 0

The process would be:

For
`x=0`

`y=-10(0)+200\\y=200`

For
`y=0`

`y=-10x+200\\0=-10x+200\\-200=-10x\\(-200)/(-10) =x\\x=20`

With these values we can graph the linear equation, which is attached. Remember that each
`(x;y)` pair forms a point.