Question

points each)

1. y = 2x + 3

Explanation:

Step1: Identify the equation type

The equation \( y = 2x + 3 \) is in slope - intercept form (\( y=mx + b \)), where \( m = 2 \) (slope) and \( b = 3 \) (y - intercept).

Step2: Plot the y - intercept

The y - intercept \( b = 3 \) means the line crosses the y - axis at the point \( (0,3) \). Locate the point \( (0,3) \) on the coordinate plane.

Step3: Use the slope to find another point

The slope \( m = 2=\frac{2}{1} \), which means for every 1 unit we move to the right (increase in x by 1), we move up 2 units (increase in y by 2). From the point \( (0,3) \), moving 1 unit to the right (x becomes \( 0 + 1=1 \)) and 2 units up (y becomes \( 3+2 = 5 \)), we get the point \( (1,5) \). We can also move left 1 unit (x becomes \( 0-1=- 1 \)) and down 2 units (y becomes \( 3 - 2=1 \)) to get the point \( (-1,1) \).

Step4: Draw the line

Draw a straight line passing through the points we found (e.g., \( (0,3) \), \( (1,5) \), \( (-1,1) \)) to graph the line \( y = 2x+3 \).

Answer:

To graph \( y = 2x + 3 \):

1. Plot the y - intercept at \( (0,3) \).
2. Use the slope \( m = 2 \) to find additional points (e.g., \( (1,5) \) by moving 1 right and 2 up from \( (0,3) \), or \( (-1,1) \) by moving 1 left and 2 down from \( (0,3) \)).
3. Draw a straight line through these points.