Linear Equations

Solve for y

100

The slope-intercept form of 2x + 3y = 12. 

A. y = 3/2 x + 4           B. y = -3/2 x + 4 

C. y = 2/3 x + 4           D. y = -2/3 x + 4

D. y = -2/3 x + 4 What is D?

200

The slope-intercept form of 5x + 3y = -15. 

A. y = -3/5 x - 5             B. y = 3/5 x - 5 

C. y = -5/3 x - 5             D. y = 5/3 x - 5

C. y = -5/3 x - 5 

300

The slope-intercept form of 6x - 3y = -18. 

A. y = -2x + 6              B. y = 2x + 6 

C. y = -2x - 6               D. y = 2x - 6

B. y = 2x + 6

400

The slope-intercept form of 3x - y = -15? 

A. y = -3x + 15             B. y = 3x + 15 

C. y = -3x - 15              D. y = 3x - 15

B. y = 3x + 15

500

The slope-intercept form of y - 3 = 5(x - 1)? 

A. y = 5x + 2                B. y = -5x + 2 

C. y = 5x - 2                 D. y = -5x - 2

C. y = 5x - 2

Finding Slope

100

The slope of the equation y = -3x + 5. 

A. 3                              B. -3 

C. 5                              D. -5

B. -3

200

The slope of the equation y = 1/2x + 7. 

A. 7                             B. -7 

C. 1/2                          D. -1/2

C. 1/2

300

The slope of the equation containing the points (2, 5) and (4, 3). 

A. 1                               B. -1 

C. 3                               D. 1/3

B. -1

m = (y₂-y₁)/(x₂-x₁)

m = (3-5)/(4-2)

m = -2/2 = -1

400

The slope of the line containing the points (6, 4) and (10, 2). 

A. 4                         B. -4 

C. 1/2                      D. -1/2

D. -1/2

m = (y₂-y₁)/(x₂-x₁)

500

The slope of the line represented by the equation y - 6 = 1/3(x - 3). 

A. 1/3                          B. -1/3 

C. 7                             D. -7

A. 1/3

Intercepts

100

The y-intercept of the equation y = 7x - 5 

A. 7                          B. -7 

C. 5                          D. -5

D. -5

200

The x-intercept of the equation 3x - 8y = 24. 

A. 3                                 B. -3 

C. 8                                 D. -8

C. 8

Set y = 0 to find "x"

3x - 8(0) = 24   so   3x = 24 . 

then divide both sides by 3 .   3x/3 = 24/3

x = 8

300

The y-intercept of the equation 2x - 8y = 4 

A. 1/2                        B. -1/2 

C. 2                           D. -2

B. -1/2

400

The y-intercept of the equation y + 2 = 3(x - 5). 

A. 17                         B. -17 

C. 3                           D. -3

B. -17

substitute 0 for x and solve

y+2 = 3(zero - 5)

y+2 = -15 then subtract 2 from both sides

y = -17 .  the coordinate is (0,-17)

500

The x-intercept of the equation y = 3x - 9

What is 3?

set y = 0 and solve

0 = 3x - 9 . then add 9 to both sides

3x = 9   divide both sides by 3 .   3x/3 = 9/3

x = 3   coordinate point is (3,0)

Types of Slope

100

The slope of line that goes downhill from left to right

What is negative?

200

The slope of a line that goes uphill from left to right is

What is positive

300

The slope of a vertical line is

What is undefined?

400

The slope of a horizontal line is

What is zero?

500

The slope of the line containing the points (3, 9) and (3, 5) is

What is undefined?

Solving Equations

100

x + 6 = 18

x=12

Subtract 6 from both sides

200

3x -3 = 12

x = 5

Add 3 then divide both sides by 3

300

-4x - 4 = 12x

x = -1/4

Add 4x to 12x = 16x

then divide by 16 

-4/-16 reduces to -1/4

400

5x - 4 = 3x - 8

x = -2

Eliminate the -4 by adding 4 to both sides. Then subtract 3x from both sides.

2x = -4    x= -4/2= -2

500

3/2 x + 3/5 = 3/5 x - 39/10

x = -5

Multiply all denominators by common factor of 10 to eliminate the fractions.

3/2x(10) + 3/5(10) =  3/5x(10)  -39/10(10)-->

 15x + 6 = -39 + 6x Subtract 6 from both sides and 6x from both sides to get  9x = -45  x= -5

Graphing

100

FIND SLOPE

what is - 1

200

Y-Intercept "b" = 3

Slope "m" = +1

300

y=-2x + 6

400

y = 6

500

Use the point (3,1)

m = 1/3 

(y-1) = 1/3(x-3) use end point (3,1) x=3, y=1