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The points​ A(0,5), B(4,2), and​ C(0,2) form the vertices of a right triangle in the coordinate plane. What is the equation of the line that forms the​ hypotenuse?

The points A05 B42 and C02 form the vertices of a right triangle in the coordinate plane What is the equation of the line that forms the hypotenuse class=

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find the slope by using the equation m=y2-y1/x2-x1 and sub in the two points A and B (0,5) (4,2)
2-5/4-0
-3/4=m
Sub what you know into the equation y=mx+b
y=-3/4x+5
We know that b=5 because that is the y-intercept present on the line.
Hope this helps

The equation of the line that forms the hypotenuse is given by:

[tex]y = -\frac{3}{4}x + 5[/tex]

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The equation of a line is given by:

[tex]y = mx + b[/tex]

In which:

  • m is the slope, which is the rate of change, that is, how much y changes when x changes by 1.
  • b is the y-intercept, that is, the value of y when x = 0.

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  • The hypotenuse contains the points (0,5) and (4,2).
  • Point (0,5) means that when [tex]x = 0, y = 5[/tex], thus [tex]b = 5[/tex].

[tex]y = mx + 5[/tex]

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  • Given two points, the slope is the change in y divided by the change in x.
  • Points (0,5) and (4,2).
  • Change in y: 2 - 5 = -3.
  • Change in x: 4 - 0 = 4.

The slope is:

[tex]m = \frac{-3}{4} = -\frac{3}{4}[/tex]

Thus, the equation of the line that forms the hypotenuse is:

[tex]y = -\frac{3}{4}x + 5[/tex]

A similar problem is given at https://brainly.com/question/22566209