Final answer:
To find the equation of a line parallel to x + 5y = 3 containing the point (-1,5), we need to determine the slope of the given line and use the point-slope form of a line. The equation of the line parallel to the given line and passing through the point is y = -1/5x + 24/5.
Step-by-step explanation:
To find the equation of a line parallel to the given line x + 5y = 3, we need to find the slope of the given line first.
The given equation can be rearranged into slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.
From the equation x + 5y = 3, we can rewrite it as 5y = -x + 3 and then divide both sides by 5 to get y = -1/5x + 3/5.
The slope of this line is -1/5.
Since we want to find a line parallel to this line, the new line will have the same slope. The point (-1,5) also lies on the new line.
Using the point-slope form of a line y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope, we can substitute (-1,5) and -1/5 into the equation to find the equation of the line parallel to the given line:
y - 5 = -1/5(x - (-1))
y - 5 = -1/5(x + 1)
y - 5 = -1/5x - 1/5
y = -1/5x + 24/5