The equation ax+by=3,where a and b are constants,has a gradient of -2 and the y-intercept value of 1/2.Find the value of a and b

Please state your workings clearly.Thanks

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From the equation: `ax+by =3` we have been given some information such that

the gradient `m=-2`

and the y intercept co-ordinates are: `(0;1/2)` as x=0 on the y-axis

Rearrange the equation so that the gradient becomes apparent in the form:

`y=mx+c` where m is the gradient and c is the y-intercept:

`therefore ax+by =3` becomes

`by=-ax+3`

`therefore y= (-ax)/b+3/b`

Now substitute the values for x and y at the given co-ordinate `(0;1/2)`

`therefore 1/2= (-a(0))/b +3/b`

`therefore 1/2=3/b`

`therefore b/2=3`

`therefore b=3 times 2 = 6`

To find a:

As the gradient is m and m is the co-efficient of x, in this equation `m=(-a)/b`

We know the gradient is -2 (given)

`therefore -2 = (-a)/b`

Now substitute the value of b into this equation:

`therefore -2= (-a)/6`

`therefore -2 times 6 = -a`

`therefore -12 = -a`

`therefore a=12`

**Ans: a=12; b=6**

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