Linear Equations

Question 1

What is a linear equation?

Answer 1

An equation that makes a straight line when graphed, typically in the form y = mx + b.

Question 2

True or False: The graph of a linear equation can be a curve.

Answer 2

False

Question 3

What does ‘m’ represent in the slope-intercept form of a linear equation?

Answer 3

The slope of the line.

Question 4

Fill in the blank: The general form of a linear equation is ______.

Answer 4

Ax + By + C = 0

Question 5

What is the y-intercept in the equation y = 2x + 3?

Answer 5

3

Question 6

What is the slope of the line represented by the equation y = -4x + 1?

Answer 6

-4

Question 7

True or False: A linear equation can have more than one solution.

Answer 7

True

Question 8

What is the standard form of a linear equation?

Answer 8

Ax + By = C

Question 9

What does ‘B’ represent in the slope-intercept form of a linear equation?

Answer 9

The y-intercept.

Question 10

What is the slope of a line that is horizontal?

Answer 10

0

Question 11

What is the slope of a line that is vertical?

Answer 11

Undefined

Question 12

What is the point-slope form of a linear equation?

Answer 12

y - y1 = m(x - x1)

Question 13

If a linear equation has a slope of 2 and passes through the point (1, 3), what is its equation?

Answer 13

y - 3 = 2(x - 1)

Question 14

True or False: Two distinct linear equations can intersect at more than one point.

Answer 14

False

Question 15

What is the method called for solving systems of linear equations by substitution?

Answer 15

Substitution method

Question 16

What is the method called for solving systems of linear equations by adding or subtracting equations?

Answer 16

Elimination method

Question 17

Fill in the blank: The solution to a system of linear equations is the point where the ______ intersect.

Answer 17

lines

Question 18

What is the term for the maximum or minimum value of a linear function?

Answer 18

There is no maximum or minimum; linear functions extend infinitely.

Question 19

If the equation of a line is y = 3x + 4, what is the slope?

Answer 19

3

Question 20

What does it mean if two linear equations have the same slope and y-intercept?

Answer 20

They are the same line.

Question 21

What is the graphical representation of the equation 2x + 3y = 6?

Answer 21

A straight line.

Question 22

True or False: Linear equations can describe real-world relationships.

Answer 22

True

Question 23

What is the x-intercept in the equation 2x + 4y = 8?

Answer 23

4

Question 24

What is the term for a linear equation with no solution?

Answer 24

Inconsistent system

Question 25

What is the term for a linear equation with infinitely many solutions?

Answer 25

Dependent system

Question 26

What does it mean if the slopes of two lines are negative reciprocals?

Answer 26

The lines are perpendicular.

Question 27

What is the formula to find the slope between two points (x1, y1) and (x2, y2)?

Answer 27

m = (y2 - y1) / (x2 - x1)