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2. Given two points (3,y) and (1,4) and m = -3, a) Find the value of y if the line through the two given points is to have the indicated slope. b) Sketch the graph of the line formed.



Answer :

Intriguing456

Answer:

y = -2

Step-by-step explanation:

We are given two points:

  • (3, y)
  • (1, 4)

and the slope between them:

  • m = -3

Using this information and the definition of slope:

  • [tex]m=\dfrac{\Delta y}{\Delta x}[/tex]

we can solve for the missing y-coordinate of the first point.

First, we can rewrite the general slope definition using two points:

[tex]m = \dfrac{d-b}{c-a}[/tex]   for the points:   [tex](a,b)[/tex] and [tex](c,d)[/tex]

(Note: we can choose either point to be [tex](a,b)[/tex])

Plugging in the given values, we can solve for y:

[tex]-3 = \dfrac{y-4}{3-1}[/tex]

[tex]-3=\dfrac{y-4}{2}[/tex]

[tex]-6=y-4[/tex]

[tex]\boxed{y=-2}[/tex]

View image Intriguing456

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