Question

Which equation represents a line that passes through (5, 1) and has a slope of 1/2 ?

y-5= {1/2(x-1)
y-1/2 = 5(x-1)
y-1=1/2(x-5)
y-1= 5[x-1/2]
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Answer 1

C is a shortier version for that

Explanation:

Answer 2

Point-slope equation of this line:

`\displaystyle y - 1 = (1)/(2)(x-5)`.

Explanation:

The equation for a line in a cartesian plane can take multiple forms. This question gives

• a point on the line, and
• the slope of the line.

The point-slope form will the most appropriate.

What is the point-slope form equation of a line
`l`?

In general,

`l:\; y - y_0 = m (x - x_0)`,

where

• 
  `x_0` is the x-coordinate of the given point on the line,
• 
  `y_0` is the y-coordinate of the given point on the line, and
• 
  `m` is the slope or gradient of the line.

In other words,
`(x_0,\; y_0)`the point on the line.

For this line,

• The point is
  `(5,\;1)`, where
  `x_0 = 5` and
  `y_0 = 1`.
• Gradient of the line
  `\displaystyle m = (1)/(2)`.

Thus the equation for this line:

`\displaystyle y - 1 = (1)/(2) (x - 5)`.