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line passes through the point (0, –1) and has a positive slope. Which of these points could that line pass through? Check all that apply. (12, 3) (–2, –5) (–3, 1) (1, 15) (5, –2)

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Answer:

Points passing though are (12, 3),(–2, –5) and (1, 15)

Step-by-step explanation:

For a line passing through (x₁,y₁) and (x₂,y₂) slope is given by [tex]\frac{y_2-y_1}{x_2-x_1}[/tex].

Here we have one point (0, –1), we need to check slope of all the points given.

(12, 3)

          [tex]m=\frac{3-(-1))}{12-0}=\frac{1}{4}>0[/tex]

(–2, –5)

          [tex]m=\frac{-5-(-1))}{-2-0}=\frac{-4}{-2}=2>0[/tex]

(–3, 1)

         [tex]m=\frac{1-(-1))}{-3-0}=\frac{2}{-3}=-\frac{2}{3}<0[/tex]

(1, 15)

        [tex]m=\frac{15-(-1))}{1-0}=\frac{16}{1}=16>0[/tex]

(5, –2)

        [tex]m=\frac{-2-(-1))}{5-0}=\frac{-1}{5}=-\frac{1}{5}<0[/tex]

Points with positive slope are (12, 3),(–2, –5) and (1, 15)

Using the concept of an increasing line, it is found that the line can pass through these following points: (12,3), (-2,-5) and (1,15)

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  • The equation of a line is given by:

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

In which

  • m is the slope.
  • b is the y-intercept.
  • If the slope is positive, the line is increasing.

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  • Line passes through the point (0,-1), with a positive slope. Thus, it is increasing.
  • This means that for every point (x,y), if x > 0, y > -1, and if x < 0, y < -1.
  • The points that respect these conditions are: (12,3), (-2,-5) and (1,15)

A similar problem is given at https://brainly.com/question/10026522

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