The slope of a line is the ratio of the change in the y-coordinates to the change in the x-coordinates. Use the given points to find it.
B
The y-intercept indicates the value of a function when x is equal to 0. In our case, the y-intercept is the value of a cost function when 0 tickets are bought.
C
The line is continuous, which means that x and y can have all real values. Is our data continuous?
A
y= 21x + 12.25
B
See solution.
C
No, see solution.
Practice makes perfect
We are given the line that represents the cost of ordering concert tickets online. We want to write an equation for the line in slope-intercept form. In the equation x will represent the number of tickets and y will represent the total cost.
To write the equation in slope-intercept form, we need to find slope m and y-intercept b. Let's start by calculating the slope!
y= mx + b
The line passes through the points ( x_1, y_1) = ( 0, 12.25) and ( x_2, y_2) = ( 1, 33.25). The slope of this line is the ratio of the change in the y-coordinates to the change in the x-coordinates.
m= y_2 - y_1/x_2 - x_1
Let's substitute the given coordinates into the formula and evaluate it!
The slope is 21. Therefore, we can partially fill the equation in slope-intercept form.
y= 21x + b
Now, we will find the y-intercept. The y-intercept is the y-coordinate of the point on a graph where the line crosses the y-axis. We can see that the given line crosses the y-axis at the point (0, 12.25), so the y-intercept is 12.25. With this, we can complete the equation!
y= 21x + 12.25
Now, we want to write an equation for the given situation without using the graph. To write the equation in slope-intercept form, we again need to find slope m and y-intercept b.
y= mx + b
We know that the y-intercept indicates the value of a function when x is equal to 0. That is why the y-intercept is also known as the initial value. In our case, the y-intercept is the value of a cost function when 0 tickets are bought, which is a processing fee equal to $12.25. Therefore, our y-intercept is 12.25.
y= mx + 12.25
We know that the tickets cost $21 per ticket. In our case, the slope with denominator of 1 is a rate comparing change of costs when we increase the number of tickets by 1. We know that if we buy 1 more ticket, it will cost us $21 more. Therefore, the slope is 21.
y= 21x + 12.25
We wrote the equation of the line without using the graph, only with the information about the ticket prices.
We want to determine whether this graph is a good representation of the given situation. Let's compare the graph to the given data.
The line is continuous, so x and y can have all real values. In our case, x represents the number of tickets. This is not a continuous data, because we can only have whole number of tickets, like 3 or 4. We cannot have for example 2.5 or 14 tickets. Therefore, the line is not a good representation, we should draw separate points instead.
The graph is not a good representation also for another reason. The line starts at the point (0,12.25), which represents the situation in which we buy 0 tickets and pay $12.25 fee. This is unrealistic situation, because when we buy 0 tickets — there is no need to pay any fee. This point should not be included on the graph.
