Respuesta :
Answer:
The value of a and b so that ax + by = 1 has intercept is a = [tex]\frac{1}{6}[/tex] and b = [tex]\frac{1}{8}[/tex]
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.
