Question

graph this function:
y = x + 2
click to select points on the graph.

Explanation:

Step1: Identify the y-intercept

The function is \( y = x + 2 \), which is in slope - intercept form \( y=mx + b \), where \( b \) is the y - intercept. Here, \( b = 2 \), so the line crosses the y - axis at the point \( (0,2) \).

Step2: Find another point using the slope

The slope \( m = 1 \) (since the coefficient of \( x \) is 1). The slope \( m=\frac{\text{rise}}{\text{run}}=\frac{1}{1} \). Starting from the y - intercept \( (0,2) \), if we move 1 unit up (rise) and 1 unit to the right (run), we get the point \( (1,3) \). We can also find other points. For example, when \( x = 1 \), \( y=1 + 2=3 \); when \( x=- 2 \), \( y=-2 + 2 = 0 \) (the point \( (-2,0) \)). To graph the line, we can plot the points we found (like \( (0,2) \), \( (1,3) \), \( (-2,0) \)) and then draw a straight line through them.

Answer:

To graph \( y=x + 2 \), plot the y - intercept \( (0,2) \) and use the slope \( m = 1 \) to find other points (e.g., \( (1,3) \), \( (-2,0) \)) and draw a straight line through these points.