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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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jacob193

Answer:

Point-slope equation of this line:

[tex]\displaystyle y - 1 = \frac{1}{2}(x-5)[/tex].

Step-by-step 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 [tex]l[/tex]?

In general,

[tex]l:\; y - y_0 = m (x - x_0)[/tex],

where

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

In other words, [tex](x_0,\; y_0)[/tex]the point on the line.

For this line,

  • The point is [tex](5,\;1)[/tex], where [tex]x_0 = 5[/tex] and [tex]y_0 = 1[/tex].
  • Gradient of the line [tex]\displaystyle m = \frac{1}{2}[/tex].

Thus the equation for this line:

[tex]\displaystyle y - 1 = \frac{1}{2} (x - 5)[/tex].

Answer:

C is a shortier version for that

Step-by-step explanation:

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