Answer:
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- <u><em>The two linear equations are not the same, because have different y-intercept, but are parallel because have the same slope.</em></u>
Explanation:
<u>1. The equation y = –x + 3 is in the slope-intercept form.</u>
The general slope-intercept form is: y = mx + b, where m is the slope and b is the y-intercept.
If two linear equations have the same slope (m) and y-intercept (b) they represent the same function.
By visual inspection, the slope and y-intercepts of y = –x + 3 are:
- slope: m = y = –1
- y-intercept: b = 3
<u>2. Table</u>
x y
-4 1
-2 -1
1 -4
3 -6
Calculate the slope:
- (-1 - 1) / (-2 - (-4) ) = -1
- (-4 - (-1) ) / (1 - (-2) ) = -1
- (-6 - (-4) ) / (3 - 1) = -1
Thus, this function has a constant rate of change Δy/Δx, or slipe, equal to slope of y = - x + 3.
What about the y-intercept?
You can calculate it using any point from the table. Using (1, -4):
- y = mx + b
- -4 = -1(1) + b
- -4 = -1 + b
- -4 + 1 = b
- -3 = b
- b = - 3
And the equation is y = - x - 3.
In conclusion the two linear equations are not the same, because they have different y-intercept, but are parallel because have the same slope.