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]
