(-3 0) Slope=2/3 Answer

2 min read Jun 17, 2024

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 point-slope 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.

Point-Slope Form

The point-slope 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 point-slope form, we get:

y - 0 = (2/3)(x - (-3))
Simplify the equation: Simplifying the equation, we get:

y = (2/3)(x + 3)
Rewrite in slope-intercept form (optional): If you prefer to express the equation in slope-intercept 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