Question

which of the following represent the equation of a line with the slope of 1/4 that passes through the point (-8,2)

Answer 1

y = 1/4x + 4 or y - 2 = 1/4(x + 8)

Answer 2

The equation of a line with the slope of 1/4 that passes through the point (-8,2) is
`y=(x)/(4)+4`

Solution:

Given, slope of a line is
`(1)/(4)` and a point is (-8, 2)

We have to find the line equation with above given values.

Now, we know that, point slope form of a line is

`y-y_(1)=m\left(x-x_(1)\right)`

Where, m is slope of line and
`\left(x_(1), y_(1)\right) \text { is point on that line. }`

Here in our problem,
`\mathrm{m}=(1)/(4) \text { and }\left(\mathrm{x}_(1), \mathrm{y}_(1)\right)=(-8,2)`

So, substitute above values in general form.

`\begin{array}{l}{y-2=(1)/(4)(x-(-8))} \\\\ {y-2=(1)/(4)(x+8)}\end{array}`

4(y – 2) = (x + 8)

4y – 8 = x + 8

x – 4y + 8 + 8 = 0

x – 4y + 16 = 0.

4y = x +16

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

Hence the equation of a line with the slope of 1/4 that passes through the point (-8,2) is
`y=(x)/(4)+4`