Question

graph the equation.
y = x + 3
use the graphing tool to graph the equation.
click to enlarge graph

Explanation:

Step1: Identify the equation type

The equation \( y = x + 3 \) 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 \( b=3 \) (the constant term).

Step2: Find the y - intercept

The y - intercept \( b = 3 \) means the line crosses the y - axis at the point \( (0,3) \). To find another point, we can use the slope. The slope \( m = 1=\frac{1}{1} \), which means for a change of \( \Delta x=1 \) (moving 1 unit to the right along the x - axis), \( \Delta y = 1 \) (moving 1 unit up along the y - axis). Starting from \( (0,3) \), if we move 1 unit right and 1 unit up, we get the point \( (1,4) \). We can also find the x - intercept by setting \( y = 0 \) in the equation \( y=x + 3 \). So, \( 0=x + 3 \), which gives \( x=-3 \). So the line passes through \( (-3,0) \) and \( (0,3) \) (and other points like \( (1,4) \), \( (2,5) \) etc.). When graphing, we plot these points and draw a straight line through them.

Answer:

To graph \( y=x + 3 \):

1. Plot the y - intercept at \( (0,3) \) (since when \( x = 0 \), \( y=0 + 3=3 \)).
2. Plot the x - intercept at \( (-3,0) \) (since when \( y = 0 \), \( 0=x + 3\Rightarrow x=-3 \)).
3. Draw a straight line through these two points (and extend it in both directions). The line has a slope of 1, so it rises 1 unit for every 1 unit it runs to the right.