Question

PLEASE HELP MEEEE

Nelson went to the Taste of Tacos, a festival where people come to taste a variety of tacos. The festival charges an admissions fee to attend and then charges $3 per taco. By the end of the festival, Nelson spent a total, y, of $30 and purchased 6 tacos, x. Write an equation in slope-intercept form to represent this.

Answer 1

Explanation:

To represent Nelson's expenses at the Taste of Tacos festival with an equation in slope-intercept form (y = mx + b), where y is the total cost and x is the number of tacos purchased, we can break down the cost into two components:

1. The admission fee, which is a fixed cost (b).
2. The cost per taco, which is $3 (the slope or rate, m).

Given that Nelson spent a total of $30 and purchased 6 tacos, we can set up the equation as follows:

Total Cost (y) = Cost of Admission Fee + Cost of Tacos

y = b + 3x

Now, we know that the total cost (y) is $30, and the number of tacos (x) is 6. Substituting these values into the equation, we get:

30 = b + 3(6)

Now, solve for b:

30 = b + 18

To isolate b, subtract 18 from both sides of the equation:

b = 30 - 18

b = 12

So, the equation in slope-intercept form representing Nelson's expenses at the festival is:

y = 3x + 12

Answer 2

`\sf y = 3x + 12`

Explanation:

Definition:

The slope-intercept form of a linear equation is a way of writing a linear equation in which the y-intercept and the slope of the equation are explicitly represented. The y-intercept is the point where the line crosses the y-axis, and the slope is the rate of change of the line.

The slope-intercept form of a linear equation is:

`\boxed{\sf y = mx + b}`

where:

• m is the slope of the line
• b is the y-intercept of the line

In this case, the slope of the line is $3, because Nelson pays $3 for each taco he purchases.

The y-intercept of the line is the admission fee, which we do not know. Therefore, we can write the equation as follows:

`\sf y = 3x + b`

To find the value of b, we can use the fact that Nelson spent a total of $30 and purchased 6 tacos. This means that the point (6, 30) is on the line.

We can substitute these values into the equation and solve for b:

30 = 3(6) + b

30 = 18 + b

b = 30 - 18

b = 12

Therefore, the equation that represents the total amount of money Nelson spent, y, in terms of the number of tacos he purchased, x, is:

`\sf y = 3x + 12`