Question

Suppose the equation for line a is given by 2x-5y=15. If line a and b are parallel and the point (-10, 3) lies on line b, then write the equation in slope intercept form for line b

Answer 1

Line
`b` is represented by the equation
`y = (2)/(5)\cdot x + 7`.

Explanation:

Let be line
`a` represented by
`2\cdot x - 5\cdot y = 15`, whose explicitive form is:

`5\cdot y = 2\cdot x - 15`

`y = (2)/(5)\cdot x - 3`

As line
`b` is parallel to line
`a`, its slope is equal to
`(2)/(5)`. Two lines that are parallel to each other have the same slope but different y-intercept. In addition, we know that point (-10, 3) lies on that line and we must find the y-intercept (
`k`):

`y = (2)/(5)\cdot x +k`

If
`x = -10` and
`y = 3`, then:

`3 = (2)/(5)\cdot (-10)+k`

`k = 3+(2)/(5) \cdot (10)`

`k = 7`

Line
`b` is represented by the equation
`y = (2)/(5)\cdot x + 7`.