To find the equation of a line you need to know the slope and y-intercept!

Finding the Equation of a Line

InstructionsThere are 12 practice problems in this packet.Record the answers to each problem on a sheet of

notebook paper, along with any work that may be necessary to arrive at the answers.

Check each answer before advancing to the next problem. If you get one wrong, rework it until you can get the right answer; this is a study tool after all.

Turn in your paper for an easy 100! You will not be penalized if you do not turn in your

paper; this review is to help you, not hurt you! However, if you do not take it seriously, you will only hurt yourself!

Slope-Intercept FormThe slope-intercept form of a linear

equation is…

y = mx + b

Where “m” is the slope and “b” is the y-intercept.

Writing the equation of a line when given the slope and y-intercept:Write the equation of a line with a slope of

½ and a y-intercept of -6:Answer: y = ½ x – 6

Write the equation of a line with the following characteristics: b = 2; m = -5

Answer: y = -5x + 2

Finding the Equation when given the Slope & a Point on the LineIn the equation y =

mx + b, replace y, m, & x with the values given.

Solve for b.Now that you know

the slope and y-intercept, write the equation.

Example: Find the equation of a line that passes through the point (8, -4) and has a slope of -2.

-4 = (-2)8 + b-4 = -16 + b (Add 16 to

both sides)

12 = by = -2x + 12

Practice Problem #1Which function represents the line that contains

the point (2, 12) and has a slope of -3?

A. f(x) = -3x + 6

B. f(x) = -3x + 18

C. f(x) = -3x + 34

D. f(x) = -3x + 38

Check Answer

Practice Problem #2Which graph best represents the line that

has a slope of and contains the point (4, -3)?

A. C.

B. D.

6

5

Check Answer

FINDING THE SLOPEIf you are given two points, the first step in any of

the methods is to find the slope from the two given points, using the slope formula.

Example 1: A line passes through the two points (-4, 1) and (2, 5). Find the equation of this line.

First, find the slope:

Next, use the slope & one of the points to solve for the y-intercept, b.

Now that you know the slope & y-intercept, write the equation:

3

2

6

4

)4(2

15

m

b

b

b

b

3

113

45

3

45

)2(3

25

3

11

3

2 xy Or Use

[STAT] Edit

Using the Graphing Calculator…[STAT] EditEnter the x-values of the two points in List 1

Enter the y-values of the two points in List 2

To find the equation of the line…[STAT] CALC4: LinReg[ENTER]Write the equation

on your paper.Convert the

decimal numbers to fractions use the [MATH] button; see next slide .

Converting Decimals to Fractions…Enter .6666666666

6 (all the way across the screen)

[MATH] [ENTER] [ENTER]

Enter 3.666666666666

[MATH] [ENTER] [ENTER]Write the

Equation: 3

11

3

2 xy

Practice Problem #3What is the y-intercept of

the function shown in the graph?

A. -24B. -21C. -18D. -9

(Hint: Find the equation of the line using the two points given; graph it on your calculator; view the table to find the value of y when x = 0.

Check Answer

(10, 17)

(6, 3)

Practice Problem #4Which of the following describes the line

containing the points (0, 4) and (3, -2)? A. y = -2x + 4B. y = ½ x + 6C. y = 2x + 4D. y = - ½ x + 6

Check Answer

Standard Form of a Linear Equation

The standard form of a linear equation is…

Ax + By = C

Where A is the coefficient of x, B is the coefficient of y, and C is the constant.

Converting from Slope-Intercept Form to Standard FormTo convert from y = mx + b to Ax + By = C,

move the term that includes x to the left side of the equation.

When writing linear equations in standard form, there are two things you must remember:1) The leading coefficient – which is the

coefficient of x – must be positive; and2) No fractions are allowed! To get rid of the

fractions, multiply the entire equation by the least common denominator (LCD).

Examplesy = - ½ x + 6½ x + y = 6 (Add ½ x to both

sides.)

2( ½ x + y = 6) Multiply everything x 2)

x + 2y = 12

Y = ⅓x – ½ -⅓x + y = - ½ (Subtract ⅓x from

both sides)

-6(-⅓x + y = - ½ ) (Multiply everything x -6, the LCM of 3 & 2; you multiply by -6 instead of 6 in order to cancel the leading negative.)

2x – 6y = 3

Converting from slope-intercept form to standard form is sometimes necessary because, on TAKS, they often write the answer choices in standard form.

Practice Problem #5Which equation best

represents the line shown in the graph?

A) 7x + 4y = 35B) 4x – 7y = 35C) 4x + 7y = -35D) 7x – 4y = -35

Check Answer

(0, -5)

(7, -1)

Additional Practice Problems#6) Convert this

equation to standard form:

y = ⅜x – 4

#7) Convert this equation to standard form:

y = -⅔x + ⅜

Check Answer

Check Answer

Converting from Standard Form to Slope-Intercept FormThis is a very

important skill because you cannot graph linear functions on your calculator unless the equation is written in slope-intercept form.

When converting from standard form to slope-intercept form, your objective is to get y by itself.

Example: 3x – 5y = 15

-5y = -3x + 15 (Subtract 3x from

both sides)

Y = x – 3 (Divide everything by -5)

5

3

Practice Problem #8At what point does the line 3x + 5y = 7

intersect the x-axis?Hint: Since the x-intercept is the point where the value of y = 0, replace y with 0 and solve for x.

Check Answer

Writing Equations from Tables of Data…When you are

asked to find the equation that matches a table of data, enter the data into your calculator using [STAT] EDIT and perform a linear regression.

Example, find the equation that matches this table of data.

X Y

-5 -3

0 2

5 7

10 12

Click here for the answer.

To match a Table to a Given Equation…Enter the equation

in the Y= screen of your calculator.

View the resulting table and compare it to the answer choices.

Practice Problem #9Which table best represents the function y =

2x − 6?

A. B. C.

Check Answer

X Y

-3 -12

1 4

3 0

7 -8

X Y

-1 4

3 12

4 14

7 20

X Y

-3 -12

2 -2

3 0

7 8

Practice Problem #10Matt is a speed skater. His coach recorded the following data during a timed practice period.

If Matt continues to skate at the rate shown in the table, what is the approximate distance in meters he will skate in 20 seconds?

A. 222 m B. 175 m C. 150 m D. 278 m

Time(seconds)

Distance(meters)

4.50 50

9.00 100

11.25 125

Check Answer

Practice Problem #11A math club decided to buy T-

shirts for its members.  A clothing company quoted the following prices for the T-shirts.

Which equation best describes the relationship between the total cost c, and the number of T-shirts, s?

A. c = 6.75sB. c = 7.00sC. c = 2s – 20 D. c = 15 + 6s

Number ofT-Shirts

Total Cost(dollars)

10 75

15 105

20 135

Check Answer

Practice Problem #12Which of the following tables contains values

for an equation that has a slope of 4?

A. B. C. D.

Check Answer

End Show

Answer to Example Table:y = x + 2

Back

Answer to Problem #1B. y = -3x + 18

In the equation y = mx + b, replace y, m, & x with the values given & solve for b, as shown.

Write the equation in slope-intercept form.

183

18

612

)2(312

xy

b

b

b

bmxy

Back

Answer to Problem #2:D.

In the equation y = mx + b, replace y, m, & x with the values given & solve for b, as shown.

Write the equation in slope-intercept form; enter it in Y= and hit [GRAPH].

3

1

6

5

3

13

133

)4(6

53

xy

b

b

b

bmxy

Back

Answer to Problem #3:C. -18

Enter the two points in the [STAT] EDIT screen, with the x-values going in L1 and the y-values in L2.

Perform a linear regression by using [STAT] CALC 4

The value given for b is the y-intercept.

Back

Answer to Problem #4:A. y = -2x + 4

Enter the two points in the [STAT] EDIT screen, with the x-values going in L1 and the y-values in L2.

Perform a linear regression by using [STAT] CALC 4 to find the equation.

Back

Answer to Problem #5B. 4x – 7y = 35

Convert the equation to standard form in order to find the correct answer:

The y-intercept is -5.The slope is , which

you can find by beginning at the y-intercept & counting up 4 & right 7 until you are at another identifiable point on the line.

Once you know the slope & y-intercept, you can write the equation:

7

4

57

4 xy

3574

)57

4(7

57

4

57

4

yx

yx

yx

xy

Back

Answer to Problem #6

3283

)48

3(8

48

3

48

3

yx

yx

yx

xy

Back

Answer to Problem #7

92416

)8

3

3

2(24

8

3

3

28

3

3

2

yx

yx

yx

xy

Back

Answer to Problem #8C.

3

7

73

7)0(53

753

x

x

x

yx

)0,3

7(

Back

Answer to Problem #9C. Enter the equation into the Y= screen of the calculator, view the resulting table and compare it to the answer choices.

Be careful! Every ordered pair must match up; compare ALL of them, not just one or two.

Back

Answer to Problem #10:A. 222 m

Enter the points in the [STAT] EDIT screen, with the x-values going in L1 and the y-values in L2.

Perform a linear regression by using [STAT] CALC 4 to find the equation.

Enter the equation into Y=.

View the table; find the y-coordinate when x = 20.

Back

Answer to Problem #11:D. c = 15 + 6s

Enter the points in the [STAT] EDIT screen, with the x-values going in L1 and the y-values in L2.

Perform a linear regression by using [STAT] CALC 4 to find the equation.

Back

Answer to Problem #12

B. Enter each table – one at a time – in the [STAT] EDIT screen & perform a linear regression.

Look for the table which has a slope of 4, which is table B, as indicated below.This is the

slope.

Back