Question

Which graph shows the equation c = 10+ 3t, where c is the total cost of going to the carnival and t is the number of $3 tickets purchased?

Answer 1

Answer: see the attached graph.

Explanation:

The given equation, c = 10+ 3t, is a linear function, which means that its graph is a line.

The slope of such graph is constant; it is the coefficient of the independent variable (t in this case).

The dependent variable is c, the total cost of going to the carnival.

The constant term, 10 in this case, is a fixed fee (the initial value of the function, when t = 0).

To graph such function you follow these steps:

•    Draw two perpendicular axis: the horizontal and the verical axis.

•    Label the horizontall axis with the name and units of the independent variable: number of tickets.

•    Label the vertical axis with the name and units of the dependent variable: cost in $.

•    Set the domain and range of the function.

             Domain: poossible values of t. The whole numbers [0, 1, 2, 3, ...]

             Range: whole numbers greater than or equal to 10 (since t is greater than or equal to 0) growing from 3 in 3: [10, 13, 16, 19, 22 ...]

•    Note that the function is discrete (not continuos)

•    Choose an adequate scale and do marks on every axis: in this case I will do marks of 1 unit each.

•    Mark the initial value, i.e. the cost when t = 0, which is:  c = 10 + 3t = 10 + 3(0) = 10 + 0 = 10

•    Mark other points. You may use this table:

            t              c($)

            0             10

            1              13

            2             16

            3              19

Finally, do not forget to add the title of the graph: cost of going to the carnival

With that information, you may understand the attached graph, which is just a sketch that shows some of the above mentioned features.

Answer 2

The graph which represents the given ticket to cost relationship is a straight line graph with slope 3 and y-intercept 10, as shown in the figure attached below.

What is slope-intercept form of a straight line?

If the slope of a line is m and the y-intercept is c, then the equation of that straight line is given as:

$y = mx + c$

This form is called the slope-intercept form of a straight line.

For the given case, there are two variables, the independent variable t, and the dependent variable is c  (as it's value is decided by the value of t)

The given relationship is in slope-intercept form of a straight line.

To plot straight lines on graph, we just need two value pairs.

Let we take t = 0, then we get c = 10

Let we take t = 1, then we get c = 10 + 3 = 13

Thus, two value pairs are

$(t_1, c_1) = (0, 10)\\(t_2, c_2) = (1, 13)$

Take vertical axis as axis for 'c' and take horizontal axis as axis for 't'

Plot those coordinates and connect them by a straight line.

But as number of tickets can be integer (non negative) only, thus, plot only those points on that straight line which are for t = non negative integers. So now erase that straight lines and leave those points only.

The graph is attached below.

Learn more about straight lines here:

https://brainly.com/question/380976