Question

Write the equation of a line in slope-intercept form that is parallel to the given line and passes through the point (12,-25).

y= 1/4x+2

Answer 1

`m_1 = m_2 = (1)/(4)`

And then since the new equation have the following form:

`y = m_2 x +b`

We can use the point given (x=12, y = -25) in order to find the intercept with this equation:

`-25 = (1)/(4) (12) +b`

And solving for the intercept b we got:

`-25 = 3 +b`

We subtract in both sides 3 and we got:

`b = -25-3 = -28`

And our final equation who satisfy the condition given is:

`y= (1)/(4) x -28`

Explanation:

For this case we have the following equation given:

`y = (1)/(4) x + 2`

And we want to find an equation of a line parallel to the given function and this case we need to satisfy this condition:

`m_1 = m_2 = (1)/(4)`

And then since the new equation have the following form:

`y = m_2 x +b`

We can use the point given (x=12, y = -25) in order to find the intercept with this equation:

`-25 = (1)/(4) (12) +b`

And solving for the intercept b we got:

`-25 = 3 +b`

We subtract in both sides 3 and we got:

`b = -25-3 = -28`

And our final equation who satisfy the condition given is:

`y= (1)/(4) x -28`