Question

Equation for ( 6, 13) ( 7900, 5 )

Answer 1

For this case we have that by definition, the equation of the line in the slope-intersection form is given by:

`y=mx+b`

Where:

m: It is the slope of the line

b: It is the cut-off point with the y axis

We have the following points through which the line passes:

`(x_ {1}, y_ {1}) :( 6,13)\\(x_ {2}, y_ {2}): (7900,5)`

We find the slope of the line:

`m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {5-13} {7900-6} = \frac {-8} {7894} = - \frac {4} {3947}`

Thus, the equation of the line is of the form:

`y = - \frac {4} {3947} x + b`

We substitute one of the points and find b:

`13 = - \frac {4} {3947} (6) + b\\13 = - \frac {24} {3947} + b\\13+ \frac {24} {3947} = b\\b = \frac {51335} {3947}`

Finally, the equation is:

`y = - \frac {4} {3947} x + \frac {51335} {3947}`

Answer:

`y = - \frac {4} {3947} x + \frac {51335} {3947}`