Respuesta :

For the linear equation that contains the points (-1,-4) and (6,10), we have that:

  • The y-intercept is y = -2.
  • The x-intercept is x = 1.

What is a linear function?

A linear function is modeled by:

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

In which:

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

In this problem, it has points (-1,-4) and (6,10), hence, considering the slope is given by change in y divided by change in x, we have that:

[tex]m = \frac{10 - (-4)}{6 - (-1)} = 2[/tex]

Then:

[tex]y = 2x + b[/tex]

Point (6,10) means that when x = 6, y = 10, and this is used to find b.

[tex]y = 2x + b[/tex]

[tex]10 = 2(6) + b[/tex]

[tex]b = -2[/tex]

The function is:

[tex]y = 2x - 2[/tex]

The y-intercept is y = -2.

For the x-intercept, we have that:

[tex]2x - 2 = 0[/tex]

[tex]x = 1[/tex]

The x-intercept is x = 1.

You can learn more about linear equations at https://brainly.com/question/24808124

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