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Step-by-step explanation:

Lanuel

The equation of the line that goes through the given points is y = -8x + 25.

Given the following points:

  • Points on the x-axis = (2, 3)
  • Points on the y-axis = (9, 1)

To determine the equation of the line that goes through the given points:

First of all, we would determine the slope of this line by using the following formula;

[tex]Slope. \;m = \frac{Change \; in \; y \;axis}{Change \; in \; x \;axis} \\\\Slope. \;m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Substituting the points into the formula, we have;

[tex]Slope, \;m = \frac{1 - 9}{3 - 2}\\\\Slope, \;m = \frac{-8}{1}\\\\[/tex]

Slope, m = -8

Now, we can determine the equation of the line by using this formula:

[tex]y-y_1 =m(x-x_1)\\\\y-9=-8(x-2)\\\\y-9=-8x+16\\\\y=-8x+16+9[/tex]

y = -8x + 25

Read more on slope here: https://brainly.com/question/3493733

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