Question

20 graph the equation: $y = 2x + 3$

Explanation:

Step1: Identify the slope and y-intercept

The equation \( y = 2x + 3 \) is in slope - intercept form \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. Here, \( m = 2=\frac{2}{1} \) and \( b = 3 \).

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 \( m=\frac{2}{1} \) 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). Starting from \( (0,3) \), if we move 1 unit to the right (to \( x = 1 \)) and 2 units up, we get to the point \( (1,3 + 2)=(1,5) \). We can also move left and down: from \( (0,3) \), moving 1 unit left ( \( x=- 1 \)) and 2 units down ( \( y = 3-2 = 1 \)) gives the point \( (-1,1) \).

Step4: Draw the line

Connect the points (e.g., \( (0,3) \), \( (1,5) \), \( (-1,1) \)) with a straight line. This line represents the graph of the equation \( y = 2x+3 \).

Answer:

The graph of \( y = 2x + 3 \) is a straight line with a y - intercept at \( (0,3) \) and a slope of 2, passing through points like \( (1,5) \) and \( (-1,1) \) (and others found using the slope - intercept form and slope properties).