To find the point-slope form of a line with a given slope and a specific point that lies on the line, follow these steps:
1. Identify the components:
- Slope (m): The slope of the line is given as [tex]\(\frac{3}{2}\)[/tex].
- Point (x₁, y₁): The given point through which the line passes is [tex]\((-1, 2)\)[/tex].
2. Point-Slope Form Equation:
The point-slope form of the equation of a line is given by:
[tex]\[
y - y_1 = m(x - x_1)
\][/tex]
where [tex]\( m \)[/tex] is the slope, and [tex]\((x_1, y_1)\)[/tex] is the point on the line.
3. Substitute the given values into the equation:
- Here, [tex]\( m = \frac{3}{2} \)[/tex]
- And the point is [tex]\((x_1, y_1) = (-1, 2)\)[/tex]
4. Implement the substitution into the point-slope form:
[tex]\[
y - 2 = \frac{3}{2}(x - (-1))
\][/tex]
5. Simplify the expression:
- The term [tex]\( x - (-1) \)[/tex] simplifies to [tex]\( x + 1 \)[/tex]:
[tex]\[
y - 2 = \frac{3}{2}(x + 1)
\][/tex]
Therefore, the point-slope form of the line with slope [tex]\(\frac{3}{2}\)[/tex] that passes through the point [tex]\((-1, 2)\)[/tex] is:
A. [tex]\( y - 2 = \frac{3}{2}(x + 1) \)[/tex]
