you receive a $30 gift card to a shop that sells fruit smoothies for $3. if you graph an equation of the line that represents the money, y, remaining on the card after you buy x smoothies, what will the y- intercept be? will the line rise or fall from left to right? explain

y = 30-3x

graph that and the other answers will be clear

To find the y-intercept of the line representing the money remaining on the gift card, we need to consider the starting amount and the number of smoothies bought.

Given that you have a $30 gift card and each smoothie costs $3, we can determine the maximum number of smoothies you can buy by dividing the total amount on the gift card by the cost of each smoothie:

Maximum number of smoothies = $30 / $3 = 10 smoothies

Since we want to represent the money remaining on the card after buying x smoothies, we can set up a table to track the amount of money remaining:

x (Number of smoothies bought) | y (Money remaining)
-----------------------------------------------------
0 | 30
1 | 27
2 | 24
3 | 21
... | ...
10 | 0

The y-intercept is the value of y when x is 0. Looking at the table, when x is 0, the money remaining is 30. Therefore, the y-intercept is 30.

Now let's analyze the line. As you buy more smoothies (i.e., as x increases), the amount of money remaining decreases, indicating a decrease in the y-values. Therefore, the line representing the money remaining on the card will fall from left to right.

In conclusion, the y-intercept is 30, and the line representing the money remaining on the gift card will fall from left to right.

To find the y-intercept of the line representing the remaining money on the gift card, you need to set x (the number of smoothies purchased) to 0. The y-intercept is the value of y when x is 0, meaning it represents the remaining money on the card before any smoothies are purchased.

Given that the gift card is worth $30, the y-intercept will be $30. This means that before purchasing any smoothies, the remaining money on the card is $30.

Now, let's determine if the line representing the remaining money will rise or fall from left to right. Since each smoothie costs $3, for each smoothie purchased, $3 will be deducted from the remaining money. Thus, as you move to the right (increasing the number of smoothies purchased) on the x-axis, the remaining money will decrease.

Therefore, the line representing the remaining money on the card will fall from left to right on the graph.