Graph the line with the given slope \( m \) and \( y \)-intercept \( b \). \( m=2, b=-2 \)

To graph the line with slope \( m = 2 \) and \( y \)-intercept \( b = -2 \), start by plotting the y-intercept. This is the point where the line crosses the y-axis, at (0, -2). From there, use the slope to find another point. Since the slope is 2, which can be represented as \( \frac{2}{1} \), rise 2 units up and run 1 unit to the right from the y-intercept. This gives you the point (1, 0). Connect these two points with a straight line, and you'll have your graph! Here's a fun fact: the concept of the slope and y-intercept comes from the classic linear equation \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. This format not only simplifies graphing but also shows how changes in \( x \) directly affect \( y \), keeping math interconnected and interesting! For those looking to sharpen their graphing skills, try practicing with different slopes and y-intercepts. Plotting lines with negative slopes or zero slope adds variety - a slope of -1 would move down as you go right, creating a whole new visual story. Always remember: every line tells its own tale in the graphing universe!