The equation y = 3x + 2 represents a line that passes through which quadrants?

The equation y = 3x + 2 is a linear equation and represents a straight line on a graph.

Step 1: Identify the slope and y-intercept of the line. The slope of the line is 3 and the y-intercept is 2.

Step 2: Plot the y-intercept on the graph. The y-intercept is the point where the line crosses the y-axis. In this case, the line crosses the y-axis at y = 2.

Step 3: Use the slope to find another point on the line. The slope is the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. A slope of 3 means that for every 1 unit increase in x, y increases by 3 units. So, starting from the y-intercept (0, 2), if we move 1 unit to the right (increase x by 1), we need to move 3 units up (increase y by 3). This gives us another point on the line: (1, 5).

Step 4: Draw the line that passes through the points identified in steps 2 and 3.

Step 5: Identify the quadrants through which the line passes. The quadrants of a graph are numbered counterclockwise from the upper right. The line y = 3x + 2 passes through the 1st quadrant (where both x and y are positive) and the 3rd quadrant (where both x and y are negative).