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Sagot :
The equation of the line that contains (−6, 19) and (−15, 28), in standard form, is: x + y = 13
Recall:
- Equation of a line can be written in standard from as Ax + By = C, where Ax and By are all terms of variable x and y, and C is a constant.
- The equation of a line in point-slope, [tex]y - y_1 = m(x - x_1)[/tex], can be rewritten in the standard form.
- Slope (m) = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
Given: (−6, 19) and (−15, 28)
Find the slope (m):
[tex]m = \frac{28 - 19}{-15 -(-6)} = \frac{9}{-9} = -1[/tex]
Write the equation in point-slope form by substituting m = -1 and [tex](x_1, y_1) = (-6, 19)[/tex] into [tex]y - y_1 = m(x - x_1)[/tex].
[tex]y - 19 = -1(x - (-6))\\\\y - 19 = -1(x + 6)[/tex]
- Rewrite in standard form
[tex]y - 19 = -1(x + 6)\\\\y - 19 = -x - 6\\\\y = -x - 6 + 19\\\\y = -x + 13\\\\\mathbf{x + y = 13}[/tex]
Therefore, the equation of the line that contains (−6, 19) and (−15, 28), in standard form, is: x + y = 13
Learn more about equation of a line in standard form on:
https://brainly.com/question/19169731
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