Answer :
To determine the point-slope equation of a line with a slope of -3 that passes through the point [tex]\((-8, -4)\)[/tex], we follow these steps:
1. Point-Slope Formula: Start with the point-slope form of the equation of a line, which is:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
Here, [tex]\((x_1, y_1)\)[/tex] is a point on the line and [tex]\(m\)[/tex] is the slope.
2. Substitute the given values: We are given [tex]\((x_1, y_1) = (-8, -4)\)[/tex] and [tex]\(m = -3\)[/tex]. Plug these values into the point-slope formula.
[tex]\[ y - (-4) = -3(x - (-8)) \][/tex]
3. Simplify the equation:
- First, simplify [tex]\( y - (-4) \)[/tex] to [tex]\( y + 4 \)[/tex].
- Then, simplify [tex]\( x - (-8) \)[/tex] to [tex]\( x + 8 \)[/tex].
Substituting these simplifications in, we get:
[tex]\[ y + 4 = -3(x + 8) \][/tex]
Upon comparing this with the provided answer options, we find that the correct equation is:
[tex]\[ \boxed{y + 4 = -3(x + 8)} \][/tex]
Hence, the answer is [tex]\( \boxed{4} \)[/tex] which corresponds to option D.
1. Point-Slope Formula: Start with the point-slope form of the equation of a line, which is:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
Here, [tex]\((x_1, y_1)\)[/tex] is a point on the line and [tex]\(m\)[/tex] is the slope.
2. Substitute the given values: We are given [tex]\((x_1, y_1) = (-8, -4)\)[/tex] and [tex]\(m = -3\)[/tex]. Plug these values into the point-slope formula.
[tex]\[ y - (-4) = -3(x - (-8)) \][/tex]
3. Simplify the equation:
- First, simplify [tex]\( y - (-4) \)[/tex] to [tex]\( y + 4 \)[/tex].
- Then, simplify [tex]\( x - (-8) \)[/tex] to [tex]\( x + 8 \)[/tex].
Substituting these simplifications in, we get:
[tex]\[ y + 4 = -3(x + 8) \][/tex]
Upon comparing this with the provided answer options, we find that the correct equation is:
[tex]\[ \boxed{y + 4 = -3(x + 8)} \][/tex]
Hence, the answer is [tex]\( \boxed{4} \)[/tex] which corresponds to option D.
