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The slope of a line passing through two points (x1 , y1) and (x2, y2) is m = (y2 - y1)/(x2 - x1)
Here we have the points with the coordinates (p;q) and (p-4;q+4) .
The slope of the line passing through them is
m = (q + 4 - q)/(p - 4 - p)
The slope of the line passing through the points is -1.
To find the slope of a line, we use the formula
m = (y1 - y2)/(x1 - x2).
In this case, your p value is x and your q value is y. We know that, for any number, q1 - q2 is going to equal -4. This is because q2 is q + 4. So if q = 1, q2 = 5 and q1 - q2 = -4. Conversely, p1 - p2 is going to equal 4. This is because p2 is p -4. So if p = 1, p2 = -3 and p1 - p2 = 4.
So, this means that in our formular for the slope,
m = -4/4
m = -1
The slope of this line is -1.
We are given two points (p,q) and (p-4,q+4)
Recall that slope is defined as the change in y over the change in x.
(y - y1) / (x - x1)
Plug into that formula:
(q + 4 - q)/ (p - 4 - p)
If a line passes through 2 points, the coordinates of the points verify the equation of the line:
y = mx + n, where m is the slope and n is the y intercept.
The point (p;q) is on the line if:
q = m*p + n (1)
The point (p-4;q+4) is on the line if:
q + 4 = m(p-4) + n (2)
We'll subtract (1) from (2):
q + 4 - q = m(p-4) + n - mp - n
We'll eliminate like terms:
4 = mp - 4m - mp
-4m = 4
m = -1
The slope of the line has the value m = -1.
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