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scZoUnD [109]
3 years ago
13

A line passes through the points (6, 10) and (4, -2).

Mathematics
1 answer:
Korolek [52]3 years ago
8 0

For this case we have:

Part A:

Point 1: (x1, y1) = (6,10)\\

Point 2:(x2, y2) = (4, -2)\\

We know that the slope m is given by:

m = \frac{(y2-y1)}{(x2-x1)}\\\\m = \frac{(- 2-10)}{(4-6)}\\\\m = \frac{(- 12)}{(- 2)}\\

m = 6\\

The slope is m = 6\\

Part b:

The equation of the line in point-slope form is given by:

(y-y1) = m (x-x1)\\

Substituting the point 1 (x1, y1) = (6,10)we have:

(y-10) = 6 (x-6)\\

Thus, the point-slope equation is: (y-10) = 6 (x-6)\\

Part c:

The equation of the line in slope-intersection form is given by:

y = mx + b\\

Rewriting the equation of part b we have:

y = 6 (x-6) +10\\\\y = 6x-36 + 10\\\\y = 6x-26\\

Thus, the equation of the line in slope-intersection form is

y = 6x-26\\

Answer:

m = 6\\\\(y-10) = 6 (x-6)\\\\y = 6x-26

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