Understanding Linear Relations and Functions

The video tutorial explains how to express the relation 5a + 3b = 18 as a function b = f(a). It begins by discussing the nature of relations and functions, emphasizing that not all relations are functions. The tutorial then demonstrates solving the equation for b, resulting in b = 6 - (5/3)a, and explains the equivalent slope-intercept form. Finally, it graphically represents the function, highlighting the slope and vertical intercept.

What is a key characteristic of a function in terms of input and output?

• Every output has exactly one input.

• Every output has multiple inputs.

• Every input has exactly one output.

• Every input has multiple outputs.

In the context of the video, what does the term 'linear relation' imply?

• The graph is a horizontal line.

• The graph is a vertical line.

• The graph is a straight line.

• The graph is a curved line.

Why are all linear relations considered functions, except in one specific case?

• Because they have a vertical line graph.

• Because they have a constant output variable.

• Because they have multiple outputs for each input.

• Because they have a constant input variable.

What happens to the graph of a linear function when the input variable is a constant?

• It becomes a curved line.

• It becomes a diagonal line.

• It becomes a vertical line.

• It becomes a horizontal line.

What is the first step in solving the equation 5a + 3b = 18 for b?

• Subtract 5a from both sides.

• Subtract 3b from both sides.

• Divide both sides by 3.

• Add 5a to both sides.

After isolating the b term, what is the next step to solve for b?

• Add 18 to both sides.

• Divide both sides by 3.

• Multiply both sides by 3.

• Subtract 18 from both sides.

How can the function b = 6 - (5/3)a be alternatively written?

• b = 6 + (5/3)a

• b = 6 - (3/5)a

• b = -(5/3)a + 6

• b = (5/3)a - 6

What is the slope of the function f(a) = -(5/3)a + 6?

• 5/3

• -3/5

• -5/3

• 3/5

What is the vertical intercept of the function f(a) = -(5/3)a + 6?

• -6

• 3

• -3

• 6

How can you find another point on the line of the function f(a) = -(5/3)a + 6?

• Move up 3 units and right 5 units.

• Move down 3 units and left 5 units.

• Move down 5 units and right 3 units.

• Move up 5 units and left 3 units.