To find the equation of the line that intersects the points [tex]\((3,6)\)[/tex] and [tex]\((5,-4)\)[/tex] in point-slope form, follow these steps:
1. Determine the slope:
The slope [tex]\( m \)[/tex] of a line passing through two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is calculated using the formula:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Given the points [tex]\((3, 6)\)[/tex] and [tex]\((5, -4)\)[/tex]:
[tex]\[
m = \frac{-4 - 6}{5 - 3} = \frac{-10}{2} = -5.0
\][/tex]
2. Use the point-slope form of the equation:
The point-slope form of the equation of a line is given by:
[tex]\[
y - y_1 = m(x - x_1)
\][/tex]
Here, we use the point [tex]\((3, 6)\)[/tex] and the calculated slope [tex]\( m = -5.0 \)[/tex].
3. Substitute the point and the slope into the form:
[tex]\[
y - 6 = -5.0(x - 3)
\][/tex]
Thus, the equation of the line in the point-slope form, using the point [tex]\((3, 6)\)[/tex], is:
[tex]\[
y - 6 = -5.0(x - 3)
\][/tex]
