Final answer:
To find the equation of a line parallel to 2x+5y=10 and passing through the point (4,1), we first need to find the slope of the given line. The slope is -2/5. We then use the point-slope form of a line to find the equation: y=(-2/5)x+(13/5).
Step-by-step explanation:
To write the slope-intercept form of an equation for a line parallel to a given line, we need to find the slope of the given line first. The slope of a line is given by the coefficient of x in the equation of the line. So, for the given line 2x+5y=10, we rearrange the equation to solve for y and find the slope:
2x+5y=10
5y=-2x+10
y=(-2/5)x+2
The slope of this line is -2/5.
Now, since the line we are looking for is parallel to this line, it will have the same slope. So, the equation of the line parallel to 2x+5y=10 and passing through the point (4,1) can be written as:
y=(-2/5)x+b
Plugging in the coordinates of the given point, we can solve for b:
1=(-2/5)(4)+b
b=1+8/5=13/5
Therefore, the equation of the line is y=(-2/5)x+(13/5).