Exploring Linear Equations and Graphing Techniques

The video tutorial covers writing and graphing linear equations. It begins with defining key vocabulary terms such as slope, rate of change, and slope-intercept form. The tutorial then demonstrates how to graph linear equations using these concepts, providing examples to illustrate the process. The video concludes with a summary and reminder to complete the handout.

What is the definition of 'slope' in the context of linear equations?

• The maximum value of y on the graph

• The point where the line crosses the y-axis

• The quotient of the vertical and horizontal distances between any two points on the line

• The constant that tells how much y changes when x increases by 1

What does the 'rate of change' represent in a linear equation?

• The horizontal intercept of the graph

• The difference in y-values divided by the difference in x-values

• The initial value of y when x is zero

• The coefficient of x in the equation y = mx + b

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

• 4

• -4

• 0

• 2

How do you graph the equation y = 2x - 4 starting from the y-intercept?

• Move up 2 units and right 1 unit from the y-intercept

• Move down 2 units and left 1 unit from the y-intercept

• Start at the origin and move up 2 units and right 1 unit

• Start at the origin and move down 2 units and left 1 unit

What error is present in the equation y = -1/2x + 4 when compared to its graph?

• The y-intercept should be negative

• The slope should be positive

• The slope should be zero

• There is no error

How should you correct the graph for the equation y = -1/2x + 4?

• Graph should be vertical

• Graph should be horizontal

• Graph should show an increasing line

• Graph should show a decreasing line

What is the slope of a line that rises 3 units for every 1 unit it moves to the right?

• 3

• 1/3

• -3

• 0

If a line crosses the y-axis at 1, what is the y-intercept?

• -1

• 0

• None of the above

• 1

What is the correct equation of a line with a slope of 3 and a y-intercept of 1?

• y = -3x + 1

• y = 1x + 3

• y = 3x - 1

• y = 3x + 1

Which of the following is a method to find the slope of a line?

• Subtracting the y-intercept from the slope

• Dividing the change in y by the change in x

• Multiplying the x-intercept by the y-intercept

• Adding the x-intercept to the y-intercept