# If there is a line through the points (2,5) and (4,6) what is the value of k so that the point of coordinates (7,k) is on the line.If there is a line through the points (2,5) and (4,6) what is the...

If there is a line through the points (2,5) and (4,6) what is the value of k so that the point of coordinates (7,k) is on the line.

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The equation of the line passing through (x1, y1) and (x2, y2) is given by:

(y - y2)/(x - x2) = (y1 - y2)/(x1 - x2)

The points we have here are (2, 5) and (4, 6). The equation of the line through them is:

(y - 6)/(x - 4) = (5 - 6)/(2 - 4)

As (7, k) lies on this line substitute 7 and k for x and y resp.

(k - 6)/3 = -1/-2

=> k - 6 = 3/2

=> k = 6 + 3/2

=> k = 7.5

**The value of k = 7.5**

We'll recall the formula for the equation of a line that passes through 2 points.

(x2 - x1)/(x - x1) = (y2 - y1)/(y - y1)

We'll identify the cordinates:

x1 = 2, x2 = 4

y1 = 5, y2 = 6

We'll substitute into the formula:

(4-2)/(x - 2) = (6-5)/(y - 5)

2/(x-2) = 1/(y-5)

We'll cross multiply:

2y - 10 = x - 2

2y = x + 8

y = x/2 + 4

If the point (7,k) lies on the line , then it's coordinates verify the equation of the line:

k = 7/2 + 4

k = (7+8)/2

**k = 15/2**