09MATC Linear Functions

Question 1

What is the general form of a linear equation?

Answer 1

y = mx + b

Question 2

In the equation y = 3x + 4, what is the slope (m)?

Answer 2

3

Question 3

True or False: The y-intercept is the value of y when x is zero.

Answer 3

True

Question 4

What does the slope of a line represent?

Answer 4

The rate of change of y with respect to x.

Question 5

Fill in the blank: The point where a line crosses the y-axis is called the __________.

Answer 5

y-intercept

Question 6

How many solutions can a pair of simultaneous linear equations have?

Answer 6

0, 1, or infinitely many

Question 7

What is the graphical representation of a linear function?

Answer 7

A straight line

Question 8

If two lines are parallel, what can be said about their slopes?

Answer 8

They are equal.

Question 9

What is the solution to the system of equations: 2x + 3y = 6 and 4x + 6y = 12?

Answer 9

Infinitely many solutions

Question 10

True or False: The lines represented by the equations y = 2x + 1 and y = -2x + 3 intersect at one point.

Answer 10

True

Question 11

What method can be used to solve simultaneous equations by substituting one equation into another?

Answer 11

Substitution method

Question 12

What is the method called that involves adding or subtracting equations to eliminate a variable?

Answer 12

Elimination method

Question 13

In the equation 4x - 2y = 8, what is the y-intercept?

Answer 13

−4

Question 14

What is the slope of the line represented by the equation y = -5x + 2?

Answer 14

-5

Question 15

Fill in the blank: The intersection point of two lines is the ________ of the equations.

Answer 15

solution

Question 16

How can you determine if two lines are coincident?

Answer 16

They have the same slope and y-intercept.

Question 17

If the slopes of two lines are negative, what does that indicate about their direction?

Answer 17

Both lines decrease as x increases.

Question 18

What is the first step in solving the system of equations: 3x + 2y = 12 and x - y = 1?

Answer 18

Isolate one variable in one of the equations.

Question 19

True or False: A linear equation can have a degree higher than 1.

Answer 19

False

Question 20

What do you call a linear equation in two variables?

Answer 20

A linear function

Question 21

In the equation y = mx + b, what does ‘b’ represent?

Answer 21

The y-intercept

Question 22

What is the graphical method of solving simultaneous equations?

Answer 22

Graphing both equations and finding their intersection.

Question 23

What is the term for a system of equations with exactly one solution?

Answer 23

Consistent and independent

Question 24

If the two equations are 2x + y = 5 and 4x + 2y = 10, what is the nature of the system?

Answer 24

Dependent with infinitely many solutions

Question 25

What can be concluded if two lines have different slopes?

Answer 25

They intersect at one point.

Question 26

Fill in the blank: The standard form of a linear equation is Ax + By = C, where A, B, and C are __________.

Answer 26

Real numbers

Question 27

What do you call the point (0, b) in the equation y = mx + b?

Answer 27

Y-intercept

Question 28

If x = 3 and y = 4 is a solution to the equation 2x + 3y = 18, is this statement true or false?

Answer 28

True

Question 29

What is the process of finding the value of variables that satisfy all equations in a system called?

Answer 29

Solving the system of equations

Question 30

True or False: The lines represented by y = 2x + 1 and y = 2x + 3 are the same line.

Answer 30

False

Question 31

What do you call the slope of a line that is horizontal?

Answer 31

Zero

Question 32

What is the slope of a vertical line?

Answer 32

Undefined

Question 33

Fill in the blank: The solution to a system of equations can be found using the ________ method, elimination method, or graphing.

Answer 33

Substitution

Question 34

What does it mean for a system of equations to be inconsistent?

Answer 34

There is no solution.