Given that the line x/a + y/b = 1 passes through ( 0 , 3 ) and ( 5 , 1 ), find the value of a and b
Well, from the first data point, b had to be 3
Then
5/a+1/3=1
15+a=3a
a=7.5
check that
To find the values of a and b, we can use the information given about the line passing through the points (0, 3) and (5, 1).
The equation of a line in the slope-intercept form is given by y = mx + c, where m is the slope of the line and c is the y-intercept.
We can rewrite the equation of the given line in slope-intercept form by isolating y:
x/a + y/b = 1
y/b = 1 - x/a
y/b = (a - x)/a
Now, we can compare this with y = mx + c to determine the values of m and c.
Comparing the equations, we get:
m = 1/a
c = 0
We know that the line passes through the points (0, 3) and (5, 1). Let's substitute these coordinates into the equation:
For (0, 3):
3 = (1/a)(0) + 0
3 = 0 + 0
3 = 0
This does not provide any useful information about the values of a and b. However, let's proceed with substituting the other point.
For (5, 1):
1 = (1/a)(5) + 0
1 = 5/a
To solve for a, we can cross-multiply:
a = 5
Now, we can substitute this value back into one of the original equations to find the value of b.
Let's use the equation y/b = (a - x)/a:
1/b = (5 - 5)/5
1/b = 0/5
1/b = 0
To solve for b, we can cross-multiply:
b = 1
Therefore, the values of a and b are 5 and 1, respectively.