problem 2: part a\ncreate a graph that shows a non - proportional linear relationship with a slope of…

Explanation:

Step1: Recall non - proportional linear relationship

A non - proportional linear relationship has the form (y = mx + b) where (b\neq0) (in contrast to proportional relationship (y = mx) where (b = 0) and the line passes through the origin). The slope (m=\frac{1}{4}). Let's choose a non - zero (b), say (b = 2). So the equation of the line is (y=\frac{1}{4}x + 2).

Step2: Find two points on the line

• When (x = 0), (y=\frac{1}{4}(0)+2=2). So the point is ((0,2)).
• When (x = 4), (y=\frac{1}{4}(4)+2=1 + 2=3). So the point is ((4,3)).
• When (x = 8), (y=\frac{1}{4}(8)+2=2 + 2=4). So the point is ((8,4)). We can plot these points ((0,2)), ((4,3)), ((8,4)) on the given grid. The line passing through these points will have a slope of (\frac{1}{4}) (since the change in (y) is (1) when the change in (x) is (4)) and a (y) - intercept of (2) (so it does not pass through the origin, hence non - proportional).

Answer:

To create the graph:

1. Plot the point ((0,2)) (since when (x = 0), (y = 2) for the line (y=\frac{1}{4}x + 2)).
2. From ((0,2)), move 4 units to the right (increase (x) by 4) and 1 unit up (increase (y) by 1) to get the point ((4,3)).
3. From ((4,3)), move 4 units to the right and 1 unit up to get the point ((8,4)).
4. Draw a straight line through these points. This line represents a non - proportional linear relationship with slope (\frac{1}{4}) (since it has a (y) - intercept of (2\neq0)).