Question

A librarian finds that the number of hours spent reading a book over a month, R, is dependent on the numbers of hours a person spends at the library over the course of a month, x, and can be modeled by the function

R(x)=26+1.5x
Draw the graph of the reading function by plotting its R-intercept and another point.

Answer 1

(0,26) (4,32)

Explanation:

The function R(x)=26+1.5x is a linear equation, so its graph is a straight line that can be drawn by plotting 2 points and connecting them.

Its R intercept occurs when x=0, so

y(0)=26,

and (0,26) is the R-intercept.

To find another point, plug in another x value into the function y(x). For example, when x=4, we have

R(4)=26+1.5(4)=32.

So, (4,32) is another point on the graph of R(x).

Answer 2

The given modeled function is R(x)=26+1.5x

where R(x) is the number of hours spent reading a book over a month

and x is the number of hours a person spends at the library over the course of a month.

Representing R(x) on the y-axis and x on the x-axis,

Puttinv x=0 to get the R(x) intercept as

R=36+1.5 x 0 = 36

So, (0,36) ia a point.

Determining other-point by putting any arbitrary value of x other than 0.

Putting x=2, to get the other point

R=36+1.5 x 10 =51

So, the other point is (10,51).

Now, joining both the points to get the graph of the given linear equation as shown in the figure.