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

Answer:

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

Answer 2

Answer:

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

Solution:

Given, slope of a line is $\frac{1}{4}$ 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, $\mathrm{m}=\frac{1}{4} \text { and }\left(\mathrm{x}_{1}, \mathrm{y}_{1}\right)=(-8,2)$

So, substitute above values in general form.

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

4(y – 2) = (x + 8)

4y – 8 = x + 8

x – 4y + 8 + 8 = 0

x – 4y + 16 = 0.

4y = x +16

$y=\frac{x}{4}+4$

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