Module B: Linear Functions

Question 1

What does a linear EQUATION look like?

Answer 1

y = mx + b

Question 2

What does a linear GRAPH look like?

Answer 2

A line. Lines have a constant slope.

Question 3

What does a linear TABLE or LIST look like?

Answer 3

There is a common difference between outputs. The average rate of change NEVER varies, no matter which two points you use for A.R.C.

Question 4

What does linear CONTEXT look like?

Answer 4

Linear context has some starting point, or base amount, and increases or decreases by a fixed numerical amount.

Question 5

Slope

Answer 5

Average Rate of Change. Also known as rise over run.

Question 6

Three forms for linear functions

Answer 6

1. Slope - Intercept
2. Point-Slope
3. Standard

Question 7

Point - Slope Form

Answer 7

y - k = m(x-h)

(h,k) is a point, m is the slope.

Question 8

Standard Form

Answer 8

Ax + By = C

Question 9

List out the steps for turning standard form into slope-intercept form

Answer 9

Ax + By = C

1. Subtract Ax from both sides: By = C - Ax
2. Divide both sides by B: y = C/B - Ax/B

Question 10

How do you find x-intercept in standard form?

Answer 10

Ax + By = C

1. Substitute y = 0. So, Ax = C.
2. Divide by A. So, x= C/A

Question 11

How do you find a y-intercept in Standard Form?

Answer 11

Ax + By = C

1. Substitute x = 0. So, By = C
2. Divide both sides by B: y = C/B

Question 12

y = mx + b

What do m and b represent?

Answer 12

m = slope
b = y-intercept

Question 13

What is a system of equations?

Answer 13

A system of equations is a set of two equations (with an input x and an output y) where you find the common solution point(s): (x,y)

Question 14

What are the four methods for solving a system?

Answer 14

1. Substitution
2. Elimination
3. Graphing
4. Guess and Check

Question 15

y = 3x + 5
y = 4x-7

How should you solve this system?

Answer 15

1. Substitution: 4x - 7 = 3x + 5
   or. .
2. Graphing: Find the intersection of the two lines.

Question 16

3x - 4y = 10
2x + y = 5

How should you solve the system?

Answer 16

Elimination.

If you have desmos, use graphing.

Question 17

3x - 4y = 10
2x + y = 5

How would you begin using elimination?

Answer 17

Multiply equation #2 by four

Question 18

5x - y = 10
x = 3y + 2

How would you solve the system?

Answer 18

Substitute the second equation into the first: 5(3y+2) - y = 10.

Question 19

Describe systems of linear inequalities.

Answer 19

Graphs of two intersecting lines (solid or dotted) where the solutions are represented with intersecting shaded regions.

Question 20

What is the only method to solve systems of linear inequalities?

Answer 20

Graphing (by hand or with desmos).

Question 21

y > 3x + 5

How do you graph this by hand?

Answer 21

1. Graph y = 3x + 5 but make it dotted due to > (has no equality)
2. Shade above the line (because of greater than)
3. For a system, just do this process twice. Intersecting shades are solution.

Question 22

How can you verify if a point is a solution to a system of inequalities?

Answer 22

Two different ways:

1. Visually inspect. Check that the point is in the DOUBLE SHADED region.
2. Evaluate (x,y) into BOTH inequalities. If both are true, then (x,y) is a solution.

Question 23

How do you graph 3x + 2y <= 5?

Answer 23

1. Go from standard form to slope-intercept form: 2y <= 5 - 3x……. y <= 2.5 - 3/2 x
2. Make sure line is SOLID
3. Shade below the line

Question 24

Is (5, 10) in the solution region for:

y > 3x - 10
2x + 3y < 6

?

Answer 24

No.

1. 10 > 3(5) - 10. So 10 > 5
2. 2(5) + 3(10) < 6 ? So 40 < 6. False.

Question 25

What does the graph of y-3 = -2(x+1) look like?

Answer 25

It is a line with a slope of -2 that passes through the point (-1,3).