Exercise 30 Page 222

Let's graph the given equation first. Next, we can find our friend's account balance after 6 months using the equation. Then we can write a linear equation that represents our account balance. Finally, we can interpret the slope and the y-intercept.

Graphing the Equation

Luckily, the given equation is already in slope-intercept form. This means that we can identify the slope as 25 and the y-intercept as 250. Using this information, we can graph the equation.

Now, to find our friends account balance after 6 months let's substitute x=6 in the equation and simplify.

After 6 months our friend's account balance will be $400.

Equati̇on for Our Account Balance

Now, we will write a linear equation for our account balance. After 6 months, we want our account to have the same balance as our friend. This means our equation should pass through the point (6,400). Since we do not have more information about our bank account, let's assume that its y-intercept is 100. y= ax+ 100 To find the slope, let's substitute (6,400) and isolate a.

Since we found the slope as 50, we can complete the equation. y= 50x+ 100

Interpreting Slope and y-intercept

Since x is the number of months and y is the bank account balance in dollars, the y-intercept tells us that at the beginning our account balance was 100. x=0 ⇒ y= 100 The slope is 50, which means that each increase by 1 to the right the balance account increases by $50. Hence, we put $50 in our account every month.