Finding the Intersection of a Linear Equation and a Horizontal Line (GED Math)

Solving for Intersection Point

• 🎯 The goal is to find the point of intersection between the linear equation 2x - 5y = 7 and the horizontal line y = 5.
• 💡 Since the horizontal line is defined as y = 5, this means the y-coordinate at the intersection point must be 5.

Substitution and Solving for X

• 🔑 To find the x-coordinate, substitute y = 5 into the linear equation 2x - 5y = 7.
• ⚡ The equation becomes 2x - 5(5) = 7, which simplifies to 2x - 25 = 7.
• 📈 Adding 25 to both sides of the equation results in 2x = 32.
• ➗ Dividing both sides by 2 yields x = 16.

The Intersection Point

• ✅ The point of intersection is therefore (16, 5), with an x-value of 16 and a y-value of 5.
• 🧠 This method works because the known value of y from the horizontal line allows for direct substitution to solve for x.