Sure, let's solve the problem step-by-step to find the equation of the line that passes through the point [tex]\((-2, -8)\)[/tex] and has a slope of 3.
1. Understand the point-slope form of a line:
The point-slope form of a line is given by:
[tex]\[
y - y_1 = m(x - x_1)
\][/tex]
where [tex]\((x_1, y_1)\)[/tex] is a point on the line and [tex]\(m\)[/tex] is the slope of the line.
2. Identify the given values:
Here, the given point is [tex]\((-2, -8)\)[/tex] and the slope [tex]\(m\)[/tex] is 3.
3. Substitute the given values into the point-slope form:
Substitute [tex]\(x_1 = -2\)[/tex], [tex]\(y_1 = -8\)[/tex], and [tex]\(m = 3\)[/tex] into the equation:
[tex]\[
y - (-8) = 3(x - (-2))
\][/tex]
4. Simplify the equation:
[tex]\[
y + 8 = 3(x + 2)
\][/tex]
Distribute 3 on the right-hand side:
[tex]\[
y + 8 = 3x + 6
\][/tex]
Isolate [tex]\(y\)[/tex] by subtracting 8 from both sides:
[tex]\[
y = 3x + 6 - 8
\][/tex]
Simplify the right-hand side:
[tex]\[
y = 3x - 2
\][/tex]
So, the equation of the line is:
[tex]\[
y = 3x - 2
\][/tex]
Given the multiple-choice options, the correct answer is:
[tex]\[
y = 3x - 2
\][/tex]
