Find anequation of the line containing (3,-4) and having slope -2. If this line contains the points (2,8) and (5.b), find a and b.​

A linear equation can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If we want to have a slope equal to -2, then our line will be something like:

y = -2*x + b

Now, we also want this line to pass through the point (3, -4)

This means that when x = 3, we must have y = -4

Then:

-4 = -2*(3) + b

-4 = -6 + b

-4 + 6 = b

2 = b

Then our line is:

y = -2*x + 2

Now, the second part says that:

If this line  contains the points (2,8) and (5.b), find a and b.​

This is incorrectly written because this line clearly does not contain the point (2, 8), so i guess the actual problem is something like:

If this line  contains the points (a,8) and (5.b), find a and b.​

If the line contains the point (a, 8), this means that when y = 8, we must have x = a.

Then:

8 = -2*a + 2

8 - 2 = -2*a

6 = -2*a

6/-2 = -3 = a

a = -3

Similar reasoing for the other point, if the line contains the point (5, b), this means that when x = 5, we have y = b.

Then:

b = -2*5 + 2 = -10 + 2

b = -8