Find the equation of the line 5x+y=18 which is parallel to the line and make an intercept of 2units on the x-axis?

To find the equation of a line parallel to 5x+y=18, we first need to find the slope of the given line.

Rearranging the equation 5x+y=18 into slope-intercept form (y=mx+b) gives us y=-5x+18.

The slope of the given line is -5.

Since the line we are looking for is parallel to the given line, it will have the same slope of -5.

Now, we know the slope of the line we are looking for is -5 and it passes through the point (2,0) on the x-axis.

Using the point-slope form of a linear equation, y-y1=m(x-x1), where (x1,y1) is the point (2,0) and m is the slope (-5), we can plug in the values to find the equation of the line:

y-0=-5(x-2)
y=-5x+10

Therefore, the equation of the line parallel to 5x+y=18 and passing through the point (2,0) on the x-axis is y=-5x+10.

The equation of the given line is 5x + y = 18.

Since the required line is parallel to the given line, it will have the same slope, which is -5.

Let the equation of the required line be y = mx + c, where m = -5 and c is the y-intercept.

Given that the required line makes an intercept of 2 units on the x-axis, we have:
When x = 2, y = 0

Substituting these values in the equation y = mx + c, we get:
0 = (-5)(2) + c
c = 10

Therefore, the equation of the required line is:
y = -5x + 10