Final answer:
The equation of the line parallel to y=5/2x+31 that passes through (-10,30) is y=5/2x+55, as it maintains the slope of the original line and incorporates the new point it passes through.
Step-by-step explanation:
To find an equation of a line that is parallel to a given line and passes through a specific point, you need to ensure the slope of the new line matches the slope of the given line, since parallel lines have equal slopes. The original equation is y=5/2x+31, which has a slope of 5/2.
The new line must therefore also have a slope of 5/2. Lines parallel to one another have the same slope but different y-intercepts. The new line must pass through the point (-10, 30). To find the y-intercept of the new line, you can use the slope-intercept form of a line equation, y=mx+b, where m is the slope and b is the y-intercept.
Since we know the slope (m) is 5/2 and the coordinates of the point it must pass through (-10, 30), we can plug these values into the equation to solve for b:
y = mx + b
30 = (5/2)(-10) + b
30 = -25 + b
55 = b
So, the y-intercept (b) is 55. Therefore, the equation of the line parallel to y=5/2x+31 and passes through (-10,30) is y = 5/2x + 55.