Answer:
The given equation is in the form 2x + 5y = 8.
To find equations that are parallel to this line, we can look for equations with the same slope, 2/5.
The slope-intercept form of a line is y = mx + b, where m is the slope.
Let's look at the given options:
A. y = 2/5 + 4 (This is not in the slope-intercept form)
B. y = -2/5x + 4 (This has the same slope, -2/5, so it is parallel to the given line)
C. y - 2 = 2/5(x + 1) (This is not in the slope-intercept form)
D. y - 2 = -2/5(x - 1) (This has the opposite slope, -2/5, so it is parallel to the given line)
E. 10x + 25y = 40 (We need to rewrite this in the slope-intercept form)
To rewrite E in the slope-intercept form, we must solve for y:
25y = -10x + 40
y = (-10/25)x + 40/25
y = (-2/5)x + 8/5 (This has the same slope, -2/5, so it is parallel to the given line)
So the equations parallel to the line 2x + 5y = 8 are:
B. y = -2/5x + 4
D. y - 2 = -2/5(x - 1)
E. y = -2/5x + 8/5