The slope of the equation y = 2-3x is -3. This can be determined by observing that the equation is in slope-intercept form, y = mx + b, where m represents the slope. In this case, m = -3.
To determine if a table of values would have the same slope, we can examine the rate of change between any two points in the table. The rate of change, which is equivalent to the slope, can be calculated by finding the difference in the y-coordinates divided by the difference in the x-coordinates.
For example, let's consider the table:
x | y
---------------
1 | -1
2 | -4
3 | -7
4 | -10
To calculate the rate of change between the points (1, -1) and (2, -4), we subtract the y-coordinates and the x-coordinates:
Change in y = -4 - (-1) = -3
Change in x = 2 - 1 = 1
The rate of change (slope) = Change in y / Change in x = -3 / 1 = -3
By repeating this process for other pairs of points in the table (such as (2, -4) and (3, -7)), we can determine if the rate of change (slope) remains constant (-3 in this case). If the rate of change is consistent for all pairs of points, then the table has the same slope as the given equation.
What is the slope of the equation y=2-3x? How can you figure out if a table of values would have the same slope?
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