Understanding Linear Functions and Their Graphs

The video tutorial introduces linear functions, focusing on graphing techniques for equations of the form y = ax and y = ax + b. It explains the properties of these functions, such as passing through the origin for y = ax, and provides examples with specific equations like y = 2x and y = -1/2x. The tutorial also covers the general case of y = ax + b, detailing how to find intercepts and plot the graph. Practical tips for effective graphing are shared, emphasizing the importance of choosing appropriate points.

What is the general form of a linear function?

• y = a + bx^2

• y = a/x + b

• y = ax + b

• y = ax^2 + bx + c

In the linear function y = ax + b, what must be true about 'a'?

• a must be positive

• a can be any number

• a must be zero

• a must be non-zero

When b = 0 in the linear function y = ax + b, what is the resulting function?

• y = ax

• y = b

• y = a + b

• y = x + b

What are the coordinates of the points used to plot y = 2x?

• (0, 1) and (2, 2)

• (0, 2) and (1, 0)

• (0, 0) and (1, 2)

• (0, 0) and (1, 1)

What is the slope of the line represented by y = -1/2x?

• 1/2

• -2

• -1/2

• 2

In the general form y = ax + b, where does the graph intersect the y-axis?

• (b, 0)

• (0, b)

• (a, 0)

• (0, a)

For the function y = ax + b, what is the x-coordinate of the point where the graph intersects the x-axis?

• -b/a

• b/a

• a/b

• -a/b

What are the coordinates of the points used to plot y = 2x - 4?

• (0, -4) and (2, 0)

• (0, 4) and (-2, 0)

• (0, -4) and (-2, 0)

• (0, 4) and (2, 0)

What is the y-intercept of the function y = 3x?

• -3

• 0

• 1

• 3

What is the slope of the line represented by y = 3x?

• 1

• 2

• 3

• 4