Can someone please help. When graphing the equations y = 2x – 2, y = 2x, and y = 2x + 3, what observation can you make about the graphs. Can you make the same observation before graphing the lines? How? Thanks
The lines are parallel.
the slope-intercept form of the equation y=mx+b gives the slope.
All of these lines are y=2x+b for b=-2,0,3. They all have the same slope, so they are parallel.
When graphing the equations y = 2x – 2, y = 2x, and y = 2x + 3, you can make the observation that all three equations have the same slope, which is 2. The slope, which is represented by the coefficient of x, determines the steepness of the line. In this case, the slope of 2 means that for every unit increase in x, there will be a 2-unit increase in y.
Before graphing the lines, you can make the same observation by examining the equations' coefficients. The general form of a linear equation is y = mx + b, where m represents the slope. In all three equations given, the coefficient of x is 2, meaning the slope is 2. By identifying this common coefficient, you can conclude that all three lines will have the same slope and therefore the same steepness.
To summarize, both graphing the equations and analyzing their coefficients allow you to observe that all three lines have the same slope of 2.