Chapter 4 ReivewAdvanced Algebra 1

Various Forms of an Equation of a Line.

Slope-Intercept Form

Point-Slope Form

slope of the line

intercept

y mx b

m

b y

1 1

1 1

slope of the line

, is any point

y y m x x

m

x y

Let’s try one…

Given “m” (the slope remember!) = 2And “b” (the y-intercept) = (0, 9)

All you have to do is plug those values intoy = mx + b

The equation becomes…y = 2x + 9

Write the equation of a line after you are given the slope and y-intercept…

Given m = 2/3, b = -12,Write the equation of a line in slope-intercept

form.Y = mx + b

Y = 2/3x – 12*************************

One last example…Given m = -5, b = -1

Write the equation of a line in slope-intercept form.

Y = mx + bY = -5x - 1

Let’s do a couple more to make sure you are expert at this.

GUIDED PRACTIE

Write an equation of the line that has the given slope and y-intercept.

1. m = 3, b = 1

y = x + 13

ANSWER

2. m = –2 , b = –4

y = –2x – 4

ANSWER

3. m = – , b =34

72

y = – x +34

72

ANSWER

1) m = 3, b = -14

2) m = -½, b = 4

3) m = -3, b = -7

4) m = 1/2 , b = 0

5) m = 2, b = 4

6) m = 0, b = -3

Given the slope and y-intercept, write the equation of a line in slope-intercept form.

y = 3x - 14

y =-½x + 4

y =-3x - 7

y = ½x

y =2x + 4

y = - 3

Write an equation of the line shown in slope-intercept form.

m = ¾

b = (0,-2)

y = ¾x - 2

3) The slope of this line is 3/2?

True

False

5) Which is the slope of the line through (-2, 3) and (4, -5)?

a) -4/3b) -3/4c) 4/3d) -1/3

8) Which is the equation of a line whose slope is undefined?

a) x = -5b) y = 7c) x = yd) x + y = 0

Using point-slope form, write the equation of a line that passes through (4, 1) with slope -2.

y – y1 = m(x – x1)

y – 1 = -2(x – 4)Substitute 4 for x1, 1 for y1 and -2 for m.

Write in slope-intercept form.y – 1 = -2x + 8 Add 1 to both sides

y = -2x + 9

Using point-slope form, write the equation of a line that passes through (-1, 3) with slope 7.

y – y1 = m(x – x1)

y – 3 = 7[x – (-1)]y – 3 = 7(x + 1)

Write in slope-intercept formy – 3 = 7x + 7y = 7x + 10

Write the equation of a line in slope-intercept form that passes through points (3, -4) and (-1, 4).

y2 – y1m =x2 – x1

4--4 =

-1-3 8 –4= = –2

y2 – y1 = m(x – x1) Use point-slope form.

y + 4 = – 2(x – 3) Substitute for m, x1, and y1.

y + 4 = – 2x + 6 Distributive property

Write in slope-intercept form.y = – 2x + 2

1) (-1, -6) and (2, 6)

2) (0, 5) and (3, 1)

3) (3, 5) and (6, 6)

4) (0, -7) and (4, 25)

5) (-1, 1) and (3, -3)

Write the equation of the line in slope-intercept form that passes through each pair of points.

GUIDED PRACTICE for Examples 2 and 3

GUIDED PRACTICE

4. Write an equation of the line that passes through (–1, 6) and has a slope of 4.

y = 4x + 10

5. Write an equation of the line that passes through (4, –2) and is parallel to the line y = 3x – 1.

y = 3x – 14ANSWER

ANSWER

Write an equation of the line that passes through (5, –2) and (2, 10) in slope intercept form

SOLUTION The line passes through (x1, y1) = (5,–2) and (x2, y2) = (2, 10). Find its slope.

y2 – y1m =x2 – x1

10 – (–2) =

2 – 5 12 –3= = –4

y2 – y1 = m(x – x1) Use point-slope form.

y – 10 = – 4(x – 2) Substitute for m, x1, and y1.

y – 10 = – 4x + 8 Distributive property

Write in slope-intercept form.y = – 4x + 18

1) Which of the following equations passes through the points (2, 1) and (5, -2)?

a. y = 3/7x + 5 b. y = -x + 3c. y = -x + 2 d. y = -1/3x + 3

a) y = -3x – 3b) y = -3x + 17c) y = -3x + 11d) y = -3x + 5

9) Which is the equation of a line that passes through (2, 5) and has slope -3?

EXAMPLE 3

Write an equation in slope-intercept that is perpendicular to y = -4x + 2 and goes through the point (-2, 3)

y – y1 = m2(x – x1) Use point-slope form.

y – 3 = (x – (–2))14

Substitute for m2, x1, and y1.

y – 3 = (x +2)14 Simplify.

y – 3 = x +14

12

Distributive property

Write in slope-intercept form.

Write equations of parallel or perpendicular lines

1 7

4 2y x

y = 3 (or any number)Lines that are horizontal have a slope of zero.

They have “run” but no “rise”. The rise/run formula for slope always equals zero since rise

= o.y = mx + by = 0x + 3

y = 3This equation also describes what is happening

to the y-coordinates on the line. In this case, they are always 3.

Horizontal Lines

x = -2Lines that are vertical have no slope

(it does not exist).They have “rise”, but no “run”. The rise/run

formula for slope always has a zero denominator and is undefined.

These lines are described by what is happening to their x-coordinates. In this example, the x-

coordinates are always equal to -2.

Vertical Lines

8) Which is the equation of a line whose slope is undefined?

a) x = -5b) y = 7c) x = yd) x + y = 0

10) Which of these equations represents a line parallel to the line

2x + y = 6?

a) Y = 2x + 3b) Y – 2x = 4c) 2x – y = 8d) Y = -2x + 1

Get Graph paper.Plot this data and discover a line of best fit.

The data shows a relationship between the number of years of college and salary earned. Plot this data and create a line of best fit. Remember to pick to two points and create a line in slope-intercept form.

(Scale for x: 0 to 8, Scale for y: 0 to 50 (Go by 5’s))

Years of college 3 2 4 6 2.5 7.5 7 1 5.5 4

Salary (in $1000) 15 20 22 47 19 18 32 10 30 28

Step 2: Select two points

I selected the points (2.5, 19) and (7, 32) on that line to determine the equation of the line.

Which ones did you pick?

Step 3: Find the slope using the two points

9.25.4

13

5.27

1932

m

Step 4: Use point-slope form to make an equation.

7.119.2

3.209.232

)7(9.232

xy

xy

xy

Did you get a similar slope or y-intercept?

Prediction Equation (line of best fit) Prediction equation is

y = 2.9x + 11.7 For example, we can predict that with five

years of college education, their salary might be $26,200.

What will 8 years of college get her salary to be?

About $33,900

Ex. 2: The table below shows the heights and the corresponding ideal weights of adult women. Find a prediction equation for this relationship.

Step 1: Graph the data points.

Height (inches) 60 62 64 66 68 70 72

Weight (pounds) 105 111 123 130 139 149 158

• Draw a line that appears to be most representative of the data. That’s your line of best fit.

Step 2: Choose two points (62, 111) and (66, 130) from the line to find the slope.

8.44

19

6266

111130

m

Step 3: Now use the slope and one of the points in the slope-intercept form to find the value of b.

6.1868.4

6.186

6.297111

)62(8.4111

hw

b

b

b

bmxy Slope-intercept form

Substitute values into form.

Multiply 4.8 by 62 to simplify.

Subtract 297.6 from both sides.

Prediction equation

Ex. 3: Draw a scatterplot and a prediction equations to show how typing speed and experience are related. Predict the typing speed of a student who has 11 weeks of experience.

Step 1: Graph the data points.

Experience (weeks) 4 7 8 1 6 3 5 2 9 6 7 10

Typing Speed (wpm) 33 45 46 20 40 30 38 22 52 44 42 55

• Scale x: 0 to 10• Scale y: 0 to 60 (Go by 5’s)

Step 2: Choose two points (5, 36) and (8, 49) from the line to find the slope.

3.43

13

58

3649

m

Step 3: Now use the point-slope and one of the points to make the equation.

Now plug in 11 for x so that we can predict the speed of typing after 11 weeks.

So there speed is 61.8 words per minute