456 Review LinearEquations

Question 1

What are the 2 forms of linear equations?

Answer 1

Slope-intercept: y = mx + b

and

Point-slope: (y - y₁) = m(x - x₁)

Question 2

What do you know about these 2 lines?

y = 3x + 2

y = 3x - 4

Answer 2

They are parallel.

They have the same slope.

Question 3

What do you know about these 2 lines?

y = ⁴/₇x - 3

y = ^-7/₄x + 8

Answer 3

They are perpendicular.

Their product of their slopes is -1.

Question 4

What is the equation for a line which has an intercept of (0, 4) and is perpendicular to:

y = ⅔ x - 1

Answer 4

y = ^-3/₂x + 4

Question 5

Find the equation of the line with slope 3 that passes through point (4, 2)

Answer 5

Point-slope:

(y - 2) = 3(x - 4)

y = 3x - 10

Question 6

Find the equation of the line that is parallel to the following and has a y-intercept of 4:

y = 7x + 3

Answer 6

y = 7x + 4

Question 7

Find the equation to the line that is perpendicular to the following and passes through the origin:

y = x/2 + 5

Answer 7

slope = ½

perpendicular slope = -2

y = -2x

Question 8

Find the equation of the line which passes through:

(1, 2) and (4, 8)

Answer 8

(1, 2) and (4, 8)

slope = ⁶/₃ = 2

(y - 2) = 2(x - 1) → y = 2x

OR

(y - 8) = 2(y - 4) → y = 2x

Question 9

Are these lines parallel?

x + y = 9

x - y = 2

Answer 9

x + y = 9

y = -x + 9 → slope -1

x - y = 2

y = x - 2 → slope 1

Not parallel.

Question 10

Are these lines parallel?

y = 4x + 3

8x - 2y = 24

Answer 10

y = 4x + 3 → slope = 4

8x - 2y = 24

y = 4x - 12 → slope = 4

They are parallel.

Question 11

Are these lines parallel?

4x + 2y = 10

10x + 5y = 25

Answer 11

4x + 2y = 10

y = -2x + 5 → slope = -2

10x + 5y = 25

y = -2x + 5 → slope = -2

They are parallel and they are the same line.

Question 12

Are these lines perpendicular?

y = 6x + 9

x + 6y = 14

Answer 12

y = 6x + 9 → slope = 6

x + 6y = 14

y = ^-1/₆x + 7/3 → slope = ^-1/₆

They are perpendicular.

Question 13

Are these lines perpendicular?

y = 3x - 2

y = ^x/₃

Answer 13

y = 3x - 2 → slope = 3

y = ^x/₃ → slope = ⅓

They are not perpendicular.

Question 14

What are the graph shifts from y = x² in this equation?

y = (x² - 3) + 4

Answer 14

y = (x² - 3) + 4

The graph shifts 3 to the right and up 4.

Question 15

How do the graphs of

y = x² and

y = -(x²)

compare?

Answer 15

They are flipped across the x-axis.

Question 16

What is a function?

Answer 16

Each input value has one output value.

Question 17

How are functions shown?

Answer 17

f(x) = 2x + 3

f(4) = 11

Question 18

Can 2 different input values have the same output value?

Answer 18

Yes. y = x²

Question 19

What is the domain of

f(x) = √(x - 3) ?

Answer 19

f(x) = √(x - 3)

x [3, ∞)

^{infinity is not a real number so parentheses are used}

Question 20

What is the test for a function?

Answer 20

A Vertical Line test

Question 21

Is the graph of a circle a function?

Answer 21

No. It does not pass the vertical line test.