Find a and b so that ax + by = 1 has an x-intercept of 6 and a y-intercept of 8.

The value of a and b so that ax + by = 1 has intercept is a = and b =

Solution:

Need to find value of a and b so that line ax + by = 1 has an x intercept of 6 and y intercept of 8.

Before proceeding further let’s understand what do we mean by x intercept and y intercept.

x intercept is a point where line crosses the x axis.

In our case line ax + by = 1 have x intercept of 6, which means line ax + by = 1 crosses x axis at 6. Another catch here is at x axis , value of y is always 0.

So we can say that ax + by = 1 passes through point (6, 0), which means at y = 0, x = 6.

Substituting this value in given equation we get

a x 6 + b x 0 = 1

=> 6a = 1

=> a = 1/6

Now let’s see y intercept.

y intercept is a point where line crosses the y axis.

In our case line ax + by = 1 have y intercept of 8, which means line ax + by = 1 crosses y axis at 8. Also at y axis , value of x is always 0.

So we can say that ax + by = 1 passes through point (0, 8), which means at x = 0, y = 8.

Substituting this value in given equation we get

a x 0 + b x 8 = 1

=> 8b = 1

=> b = 1/8

Hence value of a = 1/6 and value of b = 1/8.