Respuesta :

For this case we have that the equation of a straight line in the form of an intersection is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cutoff point with the y axis

We found the slope:

[tex]m = \frac {y2-y1} {x2-x1} = \frac {8-6} {4-5} = \frac {2} {- 1} = - 2[/tex]

So, the line is:

[tex]y = -2x + b[/tex]

We find the cut point by substituting a point:

[tex]8 = -2 (4) + b\\8 = -8 + b\\b = 8 + 8\\b = 16[/tex]

Finally, the equation is:

[tex]y = -2x + 16[/tex]

We can also have the equation of the point-slope form:

[tex]y-y_ {0} = m (x-x_ {0})[/tex]

Where:

[tex](x_ {0}, y_ {0}) = (4,8)[/tex]represents a point:

So:

[tex]y-8 = -2 (x-4)[/tex]

ANswer:

[tex]y-8 = -2 (x-4)\\y = -2x + 16[/tex]