Answer:
[tex][/tex] To find an equation of a line that is parallel to the line x - 8y = 48, we need to determine the slope of the given line. The slope of a line can be found by rearranging the equation into slope-intercept form (y = mx + b), where m is the slope.
Given equation: x - 8y = 48
Rearrange to slope-intercept form: y =([tex] \frac{1}{8} [/tex])x - 6
The slope of the given line is [tex] \frac{1}{8}[/tex]). If two lines are parallel, they have the same slope. Therefore, a line parallel to x - 8y = 48 will have a slope of[tex] \frac{1}{8}[/tex]).
The equation of a line with slope m passing through a point (x1, y1) can be written as:
y - y1 = m(x - x1)
Since we only need the slope, the equation of the line parallel to x - 8y = 48 will be in the form y = ([tex] \frac{1}{8} [/tex])x + b, where b is the y-intercept.
Therefore, the equation of the line parallel to x - 8y = 48 is y = ([tex] \frac{1}{8} [/tex])x + b, where b is an arbitrary constant.