word problem

Question

1) What are the steps you need to take to find the x-and y-intercepts of a line? You must include specific details and provide one example!

2) The cost in dollars, y, of belonging to the Stay-in-Shape Health Club, including an application fee, is expressed by the equation y = 55 + 65x , for x months. Identify the slope and the y-intercept and explain what they represent in terms of this problem. Answer in a complete sentence.

3) Why must we use a solid line when graphing a linear inequality containing ≤ or ≥, and why must we use a dashed or dotted line if the inequality contains < or > ? Provide complete details.

Answer 1

1)

 

To find the x-intercepts of any function, set y=0 and solve of x.  The point will be the ordered pair (x, 0).

To find the y-intercepts of any function, set x=0 and solve for y.  The point will be the ordered pair (0, y).

 

 

2)

 

The slope is 65.  This tells you the membership cost for one month.  The y-intercept is the constant number in the function, which is 55.  55 is the cost of the application fee, since you never started the membership.

 

 

3)

 

We used a solid line when graphing an inequality because there are ordered pairs on that line which are included in the solution set (≤, ≥).  We use dashed lines for order pairs not included in the solution set of the inequality (<, >)0