Answer:
The equation of a line with the slope of 1/4 that passes through the point (-8,2) is [tex]y=\frac{x}{4}+4[/tex]
Solution:
Given, slope of a line is [tex]\frac{1}{4}[/tex] 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
[tex]y-y_{1}=m\left(x-x_{1}\right)[/tex]
Where, m is slope of line and [tex]\left(x_{1}, y_{1}\right) \text { is point on that line. }[/tex]
Here in our problem, [tex]\mathrm{m}=\frac{1}{4} \text { and }\left(\mathrm{x}_{1}, \mathrm{y}_{1}\right)=(-8,2)[/tex]
So, substitute above values in general form.
[tex]\begin{array}{l}{y-2=\frac{1}{4}(x-(-8))} \\\\ {y-2=\frac{1}{4}(x+8)}\end{array}[/tex]
4(y – 2) = (x + 8)
4y – 8 = x + 8
x – 4y + 8 + 8 = 0
x – 4y + 16 = 0.
4y = x +16
[tex]y=\frac{x}{4}+4[/tex]
Hence the equation of a line with the slope of 1/4 that passes through the point (-8,2) is [tex]y=\frac{x}{4}+4[/tex]
