Final answer:
To find a line parallel to 2x + 5y = 1 that passes through (5, -1), first find the slope from the original equation, which is -2/5. Then use the point to determine the y-intercept of the new line. The equation of the new line is y = (-2/5)x + 1.
Step-by-step explanation:
The equation of a line parallel to another can be found by ensuring they have the same slope. Given the equation 2x + 5y = 1, we first need to rewrite it in slope-intercept form y = mx + b, where m is the slope. To do this, we solve for y:
- 5y = -2x + 1
- y = (-2/5)x + 1/5
Here the slope m is -2/5. A line that is parallel to this will have the same slope. So the new equation will have the form y = (-2/5)x + b. We can find b, the y-intercept, by plugging in the coordinates (5, -1) given in the question:
- -1 = (-2/5)(5) + b
- -1 = -2 + b
- b = 1
Therefore, the equation of the line that passes through the point (5, -1) and is parallel to the original line is y = (-2/5)x + 1.