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The equation of the line passing through (1,11) and (4,5) can be expressed in the form x/a + y/b = 1. What is a?

User Hihikomori
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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.

User Junaed
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