Linear Functions |

The first degree or linear function *f *(*x*) **= mx + b** or

** m** or

The **slope** of a **linear** function is **constant**.

There are 3 possibilities for the slope of a linear function:

- if

- if

- if

- if

In depth study of the linear equation/function is covered in **lessons 3.1 - 3.4 of the Analytic Geometry MathRoom**.

The only difference between the linear function and the linear equation is that

we refer to** ***f *(*x*)** instead of y** when it's a function.

Now get a pencil, an eraser and a note book, ** copy the questions**,

If you get stuck, review the examples in the lesson, then try again.

**1) Write the letter L beside each linear function:**

a) – 5x^{2} + 3x – 2 = 0 |
b) y = 7x – 5 |
c) 4x + 2y – 17 = 0 |

d) x^{3} – 7x^{2} + 3 = 9x |
e) 4x = – 9y + 3 |
f) |

**2) Write a linear function rule to represent each situation:**

a) Harry's age (*H*) is 2 years less than 3 times Sally's age (*s*) .

b) The cost (*C*) of a car rental is $24 per day (*d*) plus a $35 fixed fee for insurance.

c) The temperature in degrees Celcius (*C*) is 5/9 of the temperature in Farenheit (*F*) minus 32°.

d) Sam (*S*) has 4 times as many baseball cards as John (*J* ).

e) The base of a rectangle is 4 cm. more than the height (*h*). Find *P*(*h*) the perimeter function.

**3) Write a linear function rule to represent the following:**

a) the line includes the points (2, *–*3), (0, 4) and (4, *–*10).

b) the line has an initial value of 7 and a rate of change (slope) of *–*2/3.

c)

d) the line with slope = *–* 8, goes through the *y*-intercept of *y* = 3*x* *–* 7.

e) the line is perpendicular to *y* = 4/3 *x* *–* 12 and goes through ( 3, *–*8).

.

1) **b, c, e** are linear functions.

**2) Write a linear function rule to represent each situation:**

a) Harry's age (*H*) is 2 years less than 3 times Sally's age (*s*).* ***H****(***s***) = 3***s*** – 2**

b) The cost (*C*) is $24 per day (*d*) plus $35 fixed fee*. ***C****(***d***) = 24***d*** + 35**

c) The temperature in Celcius is 5/9 of Farenheit minus 32°.

d) Sam (*S*) has 4 times as many baseball cards as John (*J *). *S***(***J***) = 4***J*

e) The base of a rectangle is 4 cm. more than the height (*h*). Find *P*(*h*) the perimeter function.

*h*** = height** then *h*** + 4 = base
perimeter = 2(sum of base and height)
**

**3) Write a linear function rule to represent the following:**

a) the line includes the points (2, – 3), (0, 4) and (4, – 10).

slope = , *y*-intercept = 4 (point (0, 4) is a *y*-int) so** **

b) the line has an initial value of 7 and a rate of change (slope) of – 2/3. ** **

c) slope = , using point (–1, 7) we get:

d) the line goes through the *y*-intercept of *y* = 3*x* – 7 and has slope of – 8. * f ***(***x***) = **–** 8***x*** **–** 7**

e) the line is perpendicular to *y* = 4/3 *x* – 12 and goes through ( 3, – 8).

*(all content of the MathRoom Lessons **© Tammy the Tutor; 2004 - ).*