Question

graph the following equation.
$y = x + 2$

Explanation:

Step1: Identify the equation type

The equation \( y = x + 2 \) is in slope - intercept form \( y=mx + b \), where \( m = 1 \) (slope) and \( b = 2 \) (y - intercept).

Step2: Find the y - intercept

The y - intercept is the point where \( x = 0 \). Substitute \( x = 0 \) into the equation: \( y=0 + 2=2 \). So the point \( (0,2) \) is on the line.

Step3: Use the slope to find another point

The slope \( m = 1=\frac{1}{1} \), which means for a run of 1 (change in \( x \)), the rise is 1 (change in \( y \)). Starting from \( (0,2) \), if we move 1 unit to the right ( \( x\) increases by 1) and 1 unit up ( \( y\) increases by 1), we get the point \( (1,3) \). Alternatively, we can also use \( x=- 2 \), then \( y=-2 + 2 = 0 \), so the point \( (-2,0) \) is also on the line.

Step4: Graph the line

Plot the points (e.g., \( (0,2) \) and \( (1,3) \) or \( (0,2) \) and \( (-2,0) \)) and draw a straight line through them. The given graph in the problem has a vertical line, which is incorrect. The correct graph should be a line with slope 1 passing through \( (0,2) \).

Answer:

The correct graph of \( y=x + 2 \) is a straight line with a slope of 1, passing through the point \( (0,2) \) (y - intercept) and other points like \( (1,3) \), \( (-2,0) \) etc. (The given graph in the problem is incorrect as it shows a vertical line, the correct graph should be a non - vertical line with positive slope).