Question

8. Write an equation in standard form for a line
that passes through (2, 2) and (12, -3).

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's the slope

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

According to the statement we have two points through which the line passes:

`(x_ {1}, y_ {1}): (2,2)\\(x_ {2}, y_ {2}): (12, -3)`

We found the slope:

`m = \frac {y_ {2} -y- {1}} {x_ {2} -x_ {1}} = \frac {-3-2} {12-2} = \frac {-5} {10 } = - \frac {1} {2}`

Thus, the equation is of the form:

`y = - \frac {1} {2} x + b`

We substitute one of the points and find "b":

`2 = - \frac {1} {2} (2) + b\\2 = -1 + b\\2 + 1 = b\\b = 3`

Finally, the equation is of the form:

`y = - \frac {1} {2} x + 3`

We write the equation of the standard form
`ax + by = c`

`y-3 = -\frac {1} {2} x\\2y-6 = -x\\x + 2y = 6`

ANswer:

`x + 2y = 6`