Chapter 2Section 2

State whether is a linear function. Explain.

Answer: This is a linear function because it is in the form

Answer: This is not a linear function because x has an exponent other than 1.

State whether is a linear function. Explain.

State whether is a linear function. Explain.

Answer: This is a linear function because it can be writtenas

State whether each function is a linear function. Explain.

a.

b.

c.

Answer: yes;

Answer: No; x has an exponent other than 1.

Answer: No; two variables aremultiplied together.

Meteorology The linear function

can be used to find the number of degrees Fahrenheit, f (C), that are equivalent to a given number of degrees Celsius, C.

On the Celsius scale, normal body temperature is 37C. What is normal body temperature in degrees Fahrenheit?

Original function

Substitute.

Simplify.

Answer: Normal body temperature, in degrees Fahrenheit, is 98.6F.

There are 100 Celsius degrees between the freezing and

boiling points of water and 180 Fahrenheit degrees between these two points. How many Fahrenheit degrees equal 1 Celsius degree?

Answer: 1.8F = 1C

Divide 180 Fahrenheit degrees by 100 Celsius degrees.

Meteorology The linear function can be

used to find the distance d (s) in miles from a storm,

based on the number of seconds s that it takes to

hear thunder after seeing lightning.

a. If you hear thunder 10 seconds after seeing lightning,how far away is the storm?

b. If the storm is 3 miles away, how long will it take tohear thunder after seeing lightning?

Answer: 2 miles

Answer: 15 seconds

Write in standard form. Identify A, B, and C.

Original equation

Subtract 3x from each side.

Multiply each side by –1 so

that A 0.

Answer: and

Write in standard form. Identify A, B,

and C.

Original equation

Subtract 2y from each side.

Multiply each side by –3 so that the

coefficients are all integers.

Answer: and

Write in standard form. Identify A, B, and

C.

Original equation

Subtract 4 from each side.

Divide each side by 2 so that the

coefficients have a GCF of 1.

Answer: and

Write each equation in standard form. Identify A, B,

and C.

a.

b.

c. Answer: and

Answer: and

Answer: and

Find the x-intercept and the y-intercept of the graph of

Then graph the equation.

The x-intercept is the value of x when

The x-intercept is –2. The graph crosses the

x-axis at (–2, 0).

Original equation

Substitute 0 for y.

Add 4 to each side.

Divide each side by –2.

The y-intercept is 4. The graph crosses the y-axis at (0, 4).

Likewise, the y-intercept is the value of y when

Original equation

Substitute 0 for x.

Add 4 to each side.

Use the ordered pairs to graph this equation.

Answer: The x-intercept is –2, and the y-intercept is 4.

(0, 4)

(–2, 0)

Find the x-intercept and the y-intercept of the graph of

Then graph the equation.

Answer: The x-intercept is –2, and the y-intercept is 6.