1. Which line is the flattest (or is less steep)? Why?
y = 5x -6
y = 5x + 6
y = x - 3
y = x + 3
I thought it would be the last one since it has the smallest slope
Well, yes...but both the third and last equations have a slope of 1, and so have the same "steepness" (these lines a parallel to each other)
To determine which line is the flattest or less steep, you need to consider the slope of each equation. In the given set of equations:
y = 5x - 6
y = 5x + 6
y = x - 3
y = x + 3
The slope of each equation is represented by the coefficient in front of the x term. The slope-intercept form of a line is y = mx + b, where m represents the slope.
Comparing the slopes:
1. The first equation has a slope of 5, represented by the coefficient 5 in front of x.
2. The second equation also has a slope of 5 since it also has the coefficient 5.
3. The third equation has a slope of 1 since the coefficient in front of x is 1.
4. The fourth equation also has a slope of 1.
As you correctly observed, the third and fourth equations have the smallest slopes, making them less steep compared to the first two equations. However, it is important to note that the third and fourth equations are parallel lines, meaning they have the same "steepness" since they have the same slope. Therefore, they are equally flat or less steep.
So, to answer your question, the third equation (y = x - 3) and the fourth equation (y = x + 3) are the flattest or less steep lines because they have the smallest slopes among the given options.