Answered

Explore IDNLearn.com's extensive Q&A database and find the answers you need. Get prompt and accurate answers to your questions from our community of knowledgeable experts.

Write an equation of the line, in standard form, containing the points (−6, 19) and (−15, 28).

Sagot :

Akposevictoridn

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

Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. Discover the answers you need at IDNLearn.com. Thanks for visiting, and come back soon for more valuable insights.