Question

graph the line with the equation $y = x + 1$.

Explanation:

Step1: Identify the slope and y-intercept

The equation \( y = x + 1 \) is in slope - intercept form \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. Here, \( m = 1 \) (the coefficient of \( x \)) and \( b=1 \) (the constant term).

Step2: Plot the y - intercept

The y - intercept \( b = 1 \) means the line crosses the y - axis at the point \( (0,1) \). Locate the point \( (0,1) \) on the coordinate plane.

Step3: Use the slope to find another point

The slope \( m = 1=\frac{1}{1} \), which means for every 1 unit we move to the right (increase in \( x \) by 1), we move up 1 unit (increase in \( y \) by 1). Starting from \( (0,1) \), if we move 1 unit to the right ( \( x = 0+1 = 1 \)) and 1 unit up ( \( y=1 + 1=2 \)), we get the point \( (1,2) \). We can also move in the opposite direction: from \( (0,1) \), move 1 unit to the left ( \( x=0 - 1=- 1 \)) and 1 unit down ( \( y = 1-1 = 0 \)) to get the point \( (-1,0) \).

Step4: Draw the line

Draw a straight line through the points we have plotted (e.g., \( (0,1) \), \( (1,2) \), \( (-1,0) \)). This line represents the equation \( y=x + 1 \).

Answer:

To graph \( y=x + 1 \):

1. Plot the y - intercept at \( (0,1) \).
2. Use the slope \( m = 1 \) to find another point (e.g., \( (1,2) \) or \( (-1,0) \)).
3. Draw a straight line through the plotted points.