Final answer:
To find a line parallel to 2x + 5y = 5, we need to identify the slope of the given line, which is -2/5. Any line that has this same slope will be parallel to it. Using ordered pairs such as (0,1) and (-5, 3), we can confirm that a line with these points will have the same slope and therefore be parallel.
Step-by-step explanation:
The student has asked for the line that would be parallel to the given equation 2x + 5y = 5. To find a line that is parallel to another, we need to ensure that the two lines have the same slope. First, we must write the given equation in y = mx + b form to identify its slope, where m is the slope and b is the y-intercept.
Rearranging 2x + 5y = 5 into slope-intercept form gives us y = (-2/5)x + 1. This means the slope of our line is -2/5. A line parallel to this one must have the same slope of -2/5. We can use this slope and any two preferred ordered pairs that satisfy the equation for a line with this slope. For example, if we choose the ordered pairs (0,1) and (-5, 3), we can develop the equation of a line as y = (-2/5)x + 1, which would be parallel to the given line.