Question

Draw the graph of y = x + 2 from x = –3 to x = 2.

Answer 1

1. Calculate endpoints

To draw the line segment accurately, we evaluate the function at the boundaries of the given domain:

When x = –3: y = (–3) + 2 = 1.

This gives the point (–3, –1).

When x = 2: y = (2) + 2 = 4.

This gives the point (2, 4).

2. Identify intercepts

Finding where the line crosses the axes helps in placement:

y-intercept: Set x = 0, then y = 2.

Point: (0, 2). 

x-intercept: Set y = 0, then 0 = x + 2

⇒ x = –2. 

Point: (2, 0).

3. Analyze slope

The equation is in the slope-intercept form y = mx + b, where m = 1. This means for every 1 unit moved to the right, the line rises by 1 unit.

The graph of y = x + 2 from x = –3 to x = 2 is a straight line segment starting at the point (–3, –1) and ending at the point (2, 4).