Question

A 2-column table with 6 rows. the first column is labeled x with entries negative 4, negative 3, negative 2, negative 1, 0, 1. the second column is labeled f of x with entries negative 10, 0, 0, negative 4, negative 6, 0. which is a y-intercept of the continuous function in the table? (0, �6) (�2, 0) (�6, 0) (0, �2)

Answer 1

The y-intercept is 30: (0,30)

Explanation:

It is difficult understanding the answer options. The y-intercept of the function defined by the values in the table can be found in one of two way: Graphing and Mathematically. I'll start with graphing.

Graph The Function

See the attached graph. The given points are plotted and a line is drawn through them. A small amount of trial and error yields f(x) = 10x+30. The y-intercept is thus 30.

Mathematically

We know from the graph that the points form a straight line. It will have a slope-intercept format of y = mx + b, where m is the slope and b is the y-intercept.

Lets find the slope by calculating the Rise/Run between two points. I'll choose (-3,0) and (0,30), but any two points should give the same result.

Rise = (30-0) or 30

Run = (0 - (-3)) = 3

Rise/Run (slope, m) = 10

We can now write y = 10x + b

To find b, enter any of the given points and solve for b. I'll choose point (-3,0).

y = 10x + b

0 = 10(-3) + b for (-3,0)

b = 30

The full equation for the line formed by the given points is y = 10x + 30.

Since b = 30, the y-intercept is 30. That point would be (0,30).