Finding the Equation of a Line Given a Point and Slope
This article will guide you through the process of finding the equation of a line given a point and its slope. We will use the pointslope form of a linear equation to solve this problem.
Understanding the Problem
We are given the point (3, 0) and the slope 2/3. Our goal is to determine the equation of the line that passes through this point and has this specific slope.
PointSlope Form
The pointslope form of a linear equation is:
**y  y₁ = m(x  x₁) **
where:
 m is the slope of the line
 **(x₁, y₁) ** is a point on the line
Applying the Formula

Substitute the given values: We know that m = 2/3 and (x₁, y₁) = (3, 0). Substituting these values into the pointslope form, we get:
y  0 = (2/3)(x  (3))

Simplify the equation: Simplifying the equation, we get:
y = (2/3)(x + 3)

Rewrite in slopeintercept form (optional): If you prefer to express the equation in slopeintercept form (y = mx + b), you can distribute the 2/3 and simplify:
y = (2/3)x + 2
Conclusion
Therefore, the equation of the line passing through the point (3, 0) with a slope of 2/3 is:
y = (2/3)(x + 3) or y = (2/3)x + 2