Answered

At Westonci.ca, we make it easy for you to get the answers you need from a community of knowledgeable individuals. Get expert answers to your questions quickly and accurately from our dedicated community of professionals. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

A line passes through (10,2) and (14,-22). Write the equation of the line in standard form.

Sagot :

absor201

Answer:

The equation of the line in standard form is:

[tex]6x + y = 62[/tex]

Step-by-step explanation:

Given the points

  • (10,2)
  • (14,-22)

Determining the slope between (10, 2) and (14, -22)

[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\left(x_1,\:y_1\right)=\left(10,\:2\right),\:\left(x_2,\:y_2\right)=\left(14,\:-22\right)[/tex]

[tex]m=\frac{-22-2}{14-10}[/tex]

[tex]m=-6[/tex]

The point-slope form of the line equation is  

[tex]y-y_1=m\left(x-x_1\right)[/tex]

where

  • m is the slope of the line
  • (x₁, y₁) is the point

substituting the values m = -6 and the point (10, 2) in the point-slope form of the line equation

[tex]y-y_1=m\left(x-x_1\right)[/tex]

[tex]y - 2 = -6(x - 10)[/tex]

[tex]y - 2 = -6x +60[/tex]

adding 2 to both sides

[tex]y-2+2 = -6x + 60 + 2[/tex]

[tex]y = -6x + 62[/tex]

We can write the equation in the standard form such as

Ax + By = C

Thus,

[tex]y = -6x + 62[/tex]

adding -6x to both sides

[tex]6x + y = -6x + 62 + -6x[/tex]

[tex]6x + y = 62[/tex]

Therefore, the equation of the line in standard form is:

[tex]6x + y = 62[/tex]

Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.