Understanding Linear and Affine Functions

What is the equation of a line that passes through the origin?

• y = b

• y = mx

• y = mx + b

• y = x + b

What happens to the graph of y = x if we change it to y = x + 1?

• The graph shifts one unit down.

• The graph shifts one unit up.

• The graph shifts one unit to the left.

• The graph shifts one unit to the right.

What is the effect of adding a constant 'b' to the equation y = mx?

• It changes the slope of the line.

• It reflects the graph over the x-axis.

• It rotates the line around the origin.

• It shifts the graph vertically by 'b' units.

What is the term used to describe the vertical shift of a graph?

• Rotation

• Translation

• Reflection

• Scaling

What are the coordinates of the y-intercept in the equation y = mx + b?

• (b, 0)

• (0, m)

• (0, b)

• (m, b)

In the slope-intercept form y = mx + b, what does 'm' represent?

• The y-intercept

• The slope of the line

• The vertical shift

• The x-intercept

In the equation y = mx + b, what does 'b' determine?

• The angle of the line

• The vertical position of the line

• The horizontal position of the line

• The slope of the line

How can the orientation of a non-vertical line be adjusted?

• By rotating the graph

• By scaling the graph

• By reflecting the graph over the y-axis

• By changing the values of m and b

What is the form of the equation that describes any non-vertical line?

• y = mx

• y = mx + b

• y = b

• y = x + b

What will the next lecture focus on?

• Understanding vertical translations

• Calculating the y-intercept

• Calculating the slope of a line

• Graphing linear equations