Chapter 5 Reivew

1.Given slope (m) and y-intercept (b) create the equation in slope-intercept form.

2. Look at a graph and write an equation of a line in slope-intercept form.

3. Know how to plug into point-slope form.4. Find the slope between two points.5. Write an equation of a line that passes through two points.6. Find an equation of a line that is parallel to an equation given and

also given a random point.7. Find an equation of a line given a slope and a random point.8. Decide which two lines are parallel.9. Convert an equation into standard form.10. Write an equation of a horizontal (y = #) or vertical line (x = #).11. Decide which two lines are perpendicular.12. Look at an equation of a line and find the slope of that line.

Test Topics

€

y − y1 = m(x − x1)

€

m =y2 − y1

x2 − x1

Various Forms of an Equation of a Line.

Slope-Intercept Form

Standard Form

Point-Slope Form

slope of the line

intercept

y mx b

m

b y

, , and are integers

0, must be postive

Ax By C

A B C

A A

1 1

1 1

slope of the line

, is any point

y y m x x

m

x y

Review 5.1-5.2

Let’s try one…

Given “m” (the slope remember!) = 2And “b” (the y-intercept) = +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 PRACTICE for Example 1

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 given the slope and y-intercept

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

Review 5.3-5.4Point-Slope FormStandard Form

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?

Write equation of the line in standard form that passes through (-1,5) and (1,9)

y2 – y1m =x2 – x1

9 – 5 =

1 – -1

4 2= = 2

y – 9 = 2(x – 1)

y – 9 = 2x - 2

y = 2x + 7

-2x + y = 7

-2x -2x

2x - y = -7

Write equation of the line in standard form that has a slope of ½ and passes through (4,-5).

y + 5 = ½(x – 4)

y + 5 = ½x - 2

y = ½x - 7

-x + 2y = -14

-x -x

x - 2y = 14

2y = x - 14

Multiply everything by 2 to get rid of the fraction

Write equation of the line in standard form that is parallel to y=⅔x-8 and passes through (6,4)

y – 4 = ⅔(x – 6)

y – 4 = ⅔x - 4

y = ⅔x

-2x + 3y = 0

-2x -2x

2x - 3y = 0

m = ⅔

3y = 2x Multiply everything by 3 to get rid of the fraction

EXAMPLE 2Write an equation in standard form of the line that passes through (5, 4) and has a slope of –3.

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

y – 4 = –3(x – 5) Substitute for m, x1, and y1.

y – 4 = –3x + 15 Distributive property

SOLUTION

y = –3x + 19 Write in slope-intercept form.

3x + y = 19

+3x +3x

Review 5.6Parallel vs. Perpendicular Lines

EXAMPLE 3

b. A line perpendicular to a line with slope m1 = –4 has a slope of m2 = – = . Use point-slope form with

(x1, y1) = (–2, 3)

14

1m1

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