Answer:
The value of a is 1/2.
Explanation:
To find the value of a, we need to derive the equation of the line passing through the points (1,11) and (4,5) in the form x/a + y/b = 1.
First, we need to find the slope of the line, which can be calculated using the formula:
slope (m) = (y₂ - y₁) / (x₂ - x₁)
Let's label the coordinates as follows:
(x₁, y₁) = (1, 11)
(x₂, y₂) = (4, 5)
Substituting into the formula, we get:
slope (m) = (5 - 11) / (4 - 1)
slope (m) = -6 / 3
slope (m) = -2
Now that we have the slope (m = -2), we need to find the value of a in the equation x/a + y/b = 1.
The ratio between the coefficients of x and y in this form of equation is equal to the negative reciprocal of the slope. Therefore, we have:
a/b = -1/m
Substituting the slope, we get:
a/b = -1/(-2)
a/b = 1/2
To find the value of a, we can assign any value to b. Let's assign b = 2:
a/2 = 1/2
By cross-multiplication, we find:
2a = 1
Then, solving for a:
a = 1/2
Hence, the value of a is 1/2.