Slope of the line .Calculate the slope of the line that passes through the point (p;q) and (p-4;q+4) .

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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)

=> 4/-4

=> -1

The slope of the line passing through the points is -1.

pohnpei397's profile pic

pohnpei397 | College Teacher | (Level 3) Distinguished Educator

Posted on

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.

 

Wiggin42's profile pic

Wiggin42 | Student, Undergraduate | (Level 2) Valedictorian

Posted on

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)

Simplify: 

4/ -4

= -1

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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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