Question

part b: understanding slope & intercepts

1. in the equation ( y = mx + b ), what does:

• ( m ) represent?
• ( b ) represent?

1. how do you identify a proportional relationship using:

a graph:
a table of values:
an equation:
part c: graph analysis

1. increasing vs. decreasing (graph - based)

look at the graph below:
(graph with y - axis, x - axis, and some points)
7a. is the function increasing or decreasing?
7b. how can you tell by looking at the graph?

1. intervals of increase / decrease

8a. when asked, \on which interval does the function increase?\
are you referring to ( x ) - values or ( y ) - values?
8b. why?

1. when graphing ( y = mx + b ), what do you plot first and why?

Explanation:

1. For question 6:

• Graph: A proportional relationship forms a straight line passing through the origin (0,0).
• Table: The ratio of y to x is constant for all pairs.
• Equation: It follows the form $y = kx$ (no constant term, $b=0$).

1. For question 8:

• 8a: Interval questions for function increase/decrease reference x-values.
• 8b: Functions are defined by how output (y) changes with input (x); intervals describe input ranges.

1. For question 9:

Plot the y-intercept ($b$) first. It gives a fixed starting point $(0, b)$ on the y-axis, making it easy to apply the slope ($m$) to find other points.

Answer:

6.
A graph: A straight line through (0,0)
A table of values: Constant $\frac{y}{x}$ ratio
An equation: Has form $y = kx$ ($b=0$)
8a. x-values
8b. Intervals describe input (x) ranges where y changes

1. Plot the y-intercept ($b$) first; it is a defined starting point $(0, b)$ to build the line using the slope.