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Which equation represents the line that passes through the points (2,5) and (1,3)?

A. y = -2x + 12
B. y = -2x + 9
C. y = 2x - 8
D. y = 2x + 1

1 Answer

3 votes

Answer: The correct answer is D.

Explanation:

To find the equation of the line passing through the points (2, 5) and (1, 3), we can use the point-slope form of the equation of a line:

y - y₁ = m(x - x₁)

where (x₁, y₁) are the coordinates of one of the points on the line, and m is the slope of the line.

Let's use the first point (2, 5):

y - 5 = m(x - 2)

Now, we need to find the slope (m) using the second point (1, 3):

m = (y₂ - y₁) / (x₂ - x₁)

m = (3 - 5) / (1 - 2)

m = -2 / -1

m = 2

Now that we have the slope (m = 2), we can substitute it into the equation with the coordinates of the first point (2, 5):

y - 5 = 2(x - 2)

Next, distribute the 2 on the right side:

y - 5 = 2x - 4

To isolate y, add 5 to both sides:

y = 2x - 4 + 5

Simplify:

y = 2x + 1

So, the equation that represents the line passing through the points (2, 5) and (1, 3) is:

y = 2x + 1

User Thavamani
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