Question

Give the slope-intercept form of the equation of the line that is perpendicular to

5x + 2y = 12 and contains the point (2, 3).


Hint: solve for y=mx+b in order to get the slope (m) and then substitute in the slope and the point to find b.

Answer 1

For this case we have that by definition, the equation of a line of 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

In addition, if two lines are perpendicular then the product of their slopes is -1. That is to say:

`m_ {1} * m_ {2} = - 1`

We have the following line:

`5x + 2y = 12\\2y = -5x + 12\\y = - \frac {5} {2} x + 6`

So, we have to:
`m_ {1} = - \frac {5} {2}`

We find
`m_ {2}:`

`m_ {2} = \frac {-1} {- \frac {5} {2}}\\m_ {2} = \frac {2} {5}`

Therefore, the line is of the form:

`y = \frac {2} {5} x + b`

We substitute the given point to find "b":

`3 = \frac {2} {5} (2) + b\\3 = \frac {4} {5} + b\\b = 3- \frac {4} {5}\\b = \frac {11} {5}`

Finally, the equation is:

`y = \frac {2} {5} x + \frac {11} {5}`

ANswer:

`y = \frac {2} {5} x + \frac {11} {5}`