# What is the equation of the line in the following case:A graph of z against w is plotted with z on the y-axis and w on the x-axis. This passes though ponts where the values of the variables are: z=...

What is the equation of the line in the following case:

A graph of z against w is plotted with z on the y-axis and w on the x-axis. This passes though ponts where the values of the variables are:

z= 20 and w=0

z= 0 and w=5

z = -20 and w=10

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The graph is drawn with z represented on the y-axis and w represented on the x-axis. The graph passes through the points where the values of the variables are:

z= 20 and w=0

z= 0 and w=5

z = -20 and w=10

This is equivalent to the points (0, 20), (5, 0) and (10, -20)

The equation of the line is given by `(y - 0)/(x - 5) = (20 - 0)/(0 - 5)`

=> `y/(x - 5) = -4`

=> y = -4x + 20

=> 4x + y - 20 = 0

Substituting x = 10 and y = -20 gives 40 - 20 - 20 = 0 which proves that (10, -20) also lies on the line.

**The equation of the required line is 4x + y - 20 = 0**

The standard equation of a line:

`y=mx + b`

where m is the slope of the line (ie. gradient)

and b is the y-intercept

In your problem you need to determine the value of b

So, rearrange then substitue known values into the above standard equation to solve for b. In addition, one of the points on the line is `(x, y)=(0,20)`

`b = y - mx`

`=20-(-4)(0)`

`=20`

**Therefore, the equation of the line is:**

**`y=-4x + 20` **

**or in your case,**

**`z=-4w+20` **