Question

Jacquie has 20 postcards in her collection. each time she goes on vacation she buys 8 postcards to add to her collection. The total number of postcards y can be represented by the equation y=8x+20. Complete the following statements regarding the line.

The slope of the line is ___ and the y-intercept is ___. The ___ represents the number of postcards when she began collecting and the ___ represents the number of postcards added each vacation.

Answer 1

The slope of the line is 8 and the y-intercept is 20. The y-intercept represents the number of postcards when she began collecting and the slope of the line represents the number of postcards added each vacation.

Explanation:

In order to solve this equation, it is important to recall slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept. Now, let's look at the equation given and compare it to slope-intercept form.

• y = 8x + 20
• y = mx + b

We can conclude that 8 is the slope of the line due to the fact that it has replaced m and we can also conclude that 20 is the y-intercept due to the fact that it has replaced b. Furthermore, we know from the description provided that Jacquie began with 20 postcards, and since we now know that these 20 postcards are the y-intercept, we can fill that in as our answer. This same logic can be applied with the 8 additional postcards added each vacation since we now know it is the slope of the equation.