Final answer:
The equation of the line that passes through the point (8,0) and is parallel to x-4y=20 is y = (1/4)x - 2.
Step-by-step explanation:
To find the equation of the line that is parallel to x-4y=20 and passes through the point (8,0), we first need to determine the slope of the given line. We can do this by rearranging the equation into the slope-intercept form y = mx + b, where m represents the slope. So, we have:
x - 4y = 20
Rearranging, we get:
-4y = -x + 20
y = (1/4)x - 5
The slope of the given line is 1/4. Since the line we are looking for is parallel to this line, it will have the same slope.
Now, we can use the point-slope form of a linear equation to find the equation of the line. We have:
y - y1 = m(x - x1)
Substituting the values (8,0) and m = 1/4, we get:
y - 0 = (1/4)(x - 8)
y = (1/4)x - 2
So, the equation of the line that passes through the point (8,0) and is parallel to x-4y=20 is y = (1/4)x - 2.