Answered

IDNLearn.com offers a seamless experience for finding and sharing knowledge. Whether it's a simple query or a complex problem, our experts have the answers you need.

A line intersects the points [tex][tex]$(8,2)$[/tex][/tex] and [tex][tex]$(12,-10)$[/tex][/tex].

The slope is [tex][tex]$m=-3$[/tex][/tex].

Write an equation in point-slope form using the point [tex][tex]$(8,2)$[/tex][/tex]:

[tex][tex]$y - 2 = -3(x - 8)$[/tex][/tex]

Sagot :

GinnyAnsweridn
To write the equation of a line in point-slope form using the given point [tex]\((8, 2)\)[/tex] and the slope [tex]\(m = -3\)[/tex], we follow these steps:

1. Identify the known variables:
- Point: [tex]\((x_1, y_1) = (8, 2)\)[/tex]
- Slope: [tex]\(m = -3\)[/tex]

2. Substitute these values into the point-slope form equation:
The point-slope form of the equation of a line is:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]

3. Plug in the point and the slope:
Substituting [tex]\(y_1 = 2\)[/tex], [tex]\(m = -3\)[/tex], and [tex]\(x_1 = 8\)[/tex] into the equation, we get:
[tex]\[ y - 2 = -3(x - 8) \][/tex]

Therefore, the equation of the line in point-slope form using the point [tex]\((8, 2)\)[/tex] and slope [tex]\(m = -3\)[/tex] is:
[tex]\[ y - 2 = -3(x - 8) \][/tex]

To match the template you provided:
[tex]\[ y - 2 = -3(x - 8) \][/tex]
So, we have:
[tex]\[ y - [2] = [-3](x - [8]) \][/tex]
Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! IDNLearn.com is committed to providing the best answers. Thank you for visiting, and see you next time for more solutions.