Linear Equations And Their Graphs

Question 1

How do you know that the equation y = x is a linear equation?

Answer 1

If an equation contains an x and/or a y variable, neither of which has an exponent greater than one, it is a linear equation.

Question 2

What does the graph of a linear equation look like?

Answer 2

A linear equation creates a line when graphed on a coordinate plane.

Question 3

Is y = 5 a linear equation?

Why or why not?

Answer 3

An equation is “linear” if it contains a an x and/or a y variable that do not contain an exponent greater than 1.

Question 4

Which of these equations are linear?

                y = 4               x = 2           y = x - 1

Why did you choose the equation (s) ?

Answer 4

All three are linear equations. All three equations contain an x and/or a y variable that are not raised to any power greater than one.

Question 5

What is the name of this form of equation?

                  y = mx + b

Answer 5

Slope Intercept Form

Question 6

What is the name of an equation in this form ?

                  ax + by = c

Answer 6

Standard Form

Question 7

In this equation, the 2 is the slope, m. What is another name used to describe this number in front of the x variable?

                                y = 2x + 5

Answer 7

the coefficient of x

Question 8

In the equation y = 3x + 5, 5 is the y intercept, b. What is another word used to describe the 5 in this equation ?

Answer 8

the constant

Question 9

What is true about the lines that represent these two equations?

                         y = 4x - 3
                         y = 4x + 1

Answer 9

The lines are parallel, because they have the same slope.

Question 10

What is true about the lines that represent this system of equations?
y = -2x + 1
y = 3x

Answer 10

The lines will intersect and create exactly one solution, because the lines have different slopes.

Question 11

If the constant is changed in the linear equation, y = x - 4 from -4 to 6, describe what would happen to the graphed line ?

Answer 11

The line would shift up on the y axis.

Question 12

How many units on the y axis would a line move if the y intercept is changed from a -2 to a 5 ?

Answer 12

The line would move up 7 units on the y axis.

Question 13

What happens to the line that represents the equation y = -2x + 5 if the coefficient of x is changed to a 4?

Answer 13

The line gets steeper.

Question 14

What happens to the line that represents the equation y = 1/2x - 5, if the coefficient of x is changed to 1/8 ?

Answer 14

The line will become less steep.

Question 15

What causes a system of equations to have “no solution”?

Answer 15

The equations have the same slopes, which means the lines are parallel.

Question 16

What is true of a system of equations that has “infinite solutions”?

Answer 16

The equations are the same.

Question 17

If a system of equations has a solution, how is that solution written?

Answer 17

A solution to a system is written as an “Ordered Pair”.

Question 18

What is the slope in the equation y = -x + 4 ?

Answer 18

The slope is -1.

Question 19

What is the y intercept of the equation y = -3/4x + 2 ?

Answer 19

The y intercept is 2.

Question 20

What “type of slope” is one that runs uphill from left to right on the graph?

Answer 20

Positive slope

Question 21

What “type of slope” runs downhill from left to right on the graph?

Answer 21

A negative slope.

Question 22

What “type of slope” is a line that runs across the graph horizontally?

Answer 22

Zero slope

Question 23

What “type of slope” is a line that runs vertically on the graph ?

Answer 23

Undefined or No Slope