Exploring Basic Linear Functions and Their Graphs

What does the equation y = x signify about the relationship between x and y?

• y is always half of x

• y is always twice x

• y is always the same as x

• y is unrelated to x

What is the slope of the line described by the equation y = 2x?

• -2

• 0

• 1

• 2

What happens to the slope of the line as the value of m increases in the equation y = mx?

• The slope remains constant

• The slope becomes less steep

• The slope becomes horizontal

• The slope becomes steeper

What does a slope of 0 indicate about a line?

• The line is decreasing

• The line is vertical

• The line is increasing

• The line is horizontal

In the equation y = mx + b, what effect does changing m have?

• It makes the line horizontal

• It changes the x-intercept

• It changes the slope of the line

• It changes the y-intercept

What is the slope of a line that goes downhill from left to right?

• Positive

• Negative

• Zero

• Undefined

How does the graph of y = mx + b change when b is negative?

• The line becomes less steep

• The line shifts downwards

• The line becomes steeper

• The line shifts upwards

What does the variable 'b' represent in the equation y = mx + b?

• The slope of the line

• The x-intercept of the line

• The origin point of the line

• The y-intercept of the line

Can the equation y = mx + b describe any linear function on the coordinate plane?

• No, it cannot describe horizontal lines

• No, it can only describe functions with positive slopes

• No, it can only describe functions passing through the origin

• Yes, it can describe any linear function

How can you rearrange any linear equation into the slope-intercept form y = mx + b?

• By isolating y on one side of the equation

• By eliminating the y-intercept

• By making the slope zero

• By setting x equal to 1