Question

Some students collected the data below. They will graph the data. What is the y-intercept? Your answer should be an ordered pair ( , )

Answer 1

(0, 28)

Explanation:

Overview

To answer the question given, we have to find the point on the line that goes through the points given in the table when the x-axis represents the month of the year (1 is Jan, 2 is Feb, etc.) and the y-axis represents the average temperature for that month.

Method 1

I've attached a graph of the line for reference.

When we look at the graph of the line that goes through the points given in the table, we can determine that its y-intercept is (0, 28).

Method 2

To determine the y-intercept of the line without actually graphing it, we can construct an equation using the given points.

We know that the line's slope is defined as
`\frac{\textrm{rise}}{\textrm{run}}`.

Using that information, we can solve for the line's slope by using any two of the given points. I will use the points for January (1, 42) and February (2, 56).

`\textrm{slope} = (56-42)/(2-1) = (14)/(1) = 14`

Then, we can plug this value into the point-slope form equation

`y - b = m(x - a)`

along with one of the given points
`(a,b)` -- I'll use January (1, 42):

`y-42=14(x-1)`

Next, to solve for the y-coordinate of the line's y-intercept, we can plug 0 into the equation for x and solve for y.

`y - 42 = 14(0 - 1)`

`y - 42 = 14(-1)`

`y - 42 = -14`

`y = -14 + 42`

`y = 28`

Finally, we can plug the solved y-coordinate and 0 for the x-value (because we solved for when y when x = 0) into the format of a Cartesian coordinate:

(0, 28)