What is the point-slope form of a line with slope -4 that contains the point [tex]$(-2,3)$[/tex]?

A. [tex]y - 3 = -4(x + 2)[/tex]
B. [tex]y - 3 = 4(x + 2)[/tex]
C. [tex]y + 3 = 4(x + 2)[/tex]
D. [tex]y + 3 = -4(x - 2)[/tex]



Answer :

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]