Sure! To determine the point-slope form of a line with a given slope and a point it passes through, we can follow these steps:
1. Identify the Point-Slope Form Equation: The point-slope form of a line is given by the formula:
[tex]\[
y - y_1 = m(x - x_1)
\][/tex]
where [tex]\( m \)[/tex] is the slope, and [tex]\((x_1, y_1)\)[/tex] is a point on the line.
2. Plug in the Given Values: We are given:
- Slope ([tex]\( m \)[/tex]) = -4
- Point ([tex]\(x_1, y_1\)[/tex]) = (-2, 3)
Substituting these values into the point-slope form equation, we get:
[tex]\[
y - 3 = -4(x - (-2))
\][/tex]
3. Simplify the Equation: Simplify the expression inside the parentheses:
[tex]\[
y - 3 = -4(x + 2)
\][/tex]
Therefore, the point-slope form of the line with a slope of -4 that passes through the point [tex]\((-2, 3)\)[/tex] is:
[tex]\[
y - 3 = -4(x + 2)
\][/tex]
By comparing our derived equation with the options provided, we see that the correct answer is:
A. [tex]\( y - 3 = -4(x + 2) \)[/tex]
