Certainly! To write an equation in point-slope form using the point [tex]\((3, 6)\)[/tex] and the slope [tex]\(m = -5\)[/tex], follow these steps:
1. Identify the slope [tex]\(m\)[/tex]:
The slope of the line is given as [tex]\(m = -5\)[/tex].
2. Choose a point [tex]\((x_1, y_1)\)[/tex]:
We are given the point [tex]\((3, 6)\)[/tex].
3. Point-slope form equation:
The point-slope form of a line's equation is given by:
[tex]\[
y - y_1 = m(x - x_1)
\][/tex]
4. Substitute the values into the equation:
Here, [tex]\(x_1 = 3\)[/tex], [tex]\(y_1 = 6\)[/tex], and [tex]\(m = -5\)[/tex].
[tex]\[
y - 6 = -5(x - 3)
\][/tex]
So, the equation in point-slope form using the point [tex]\((3, 6)\)[/tex] and the slope [tex]\(-5\)[/tex] is:
[tex]\[
y - 6 = -5(x - 3)
\][/tex]
Therefore, the blanks will be filled as:
[tex]\[
y - 6 = -5(x - 3)
\][/tex]
The correct point-slope form equation is:
[tex]\[
y - 6 = -5(x - 3)
\][/tex]
