What is the equation of the line that is parallel to the line 5x+2y=12 and passes through the point (-2,4)

Step-by-step explanation:

One is given the following equation.

The problem asks one to find a line that is parallel to this one, and passes through the point: . The equation of the given line is in the standard format. The easiest approach to solve this problem is to change the equation of the given line into the slope-intercept format. The solve intercept format follows the following general equation:

Where (m) is the slope of the line and (b) is the y-intercept. Manipulate the given equation such that it follows this format:

One property of parallel lines is that they have the same slope. Therefore, if one uses the slope-intercept format to represent the slope of the parallel line, then one can state the following:

Substitute a given point on this line () , and solve for (b) to find (b):

Simplify,

Inverse operations,

Substitute this back into the equation in slope-intercept form to find the equation of the parallel line:

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18