Functions
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Linear Equations

See algebra come alive — solve equations by finding where two lines cross

How many hours until you can afford that game? How many tickets do you need to sell? Solving equations is how you find unknown quantities in everyday life. What does it really mean to "solve an equation"? When you see 2x + 3 = 7, you're looking for the value of x that makes both sides equal. But there's a beautiful visual way to find that answer: graph both sides and see where they meet.

Plot y = 2x + 3 as one line and y = 7 as another. The x-coordinate where they intersect is the solution — because that's the only x where both expressions give the same value.

In this lesson, you'll solve equations visually on the graph, verify your answers algebraically, and discover the general method that works for any linear equation — all guided by an AI tutor step by step.

Graph

FAQ

What is a linear equation?
A linear equation is an equation where the variable (usually x) appears only to the first power — no squares, cubes, or other exponents. Examples: 2x + 3 = 7, 5x - 1 = 14. When graphed, each side of the equation forms a straight line.
How do I solve a linear equation graphically?
Graph both sides of the equation as separate lines. For 2x + 3 = 7, plot y = 2x + 3 and y = 7. The x-coordinate of their intersection point is the solution. In this case they cross at x = 2, so x = 2 is the answer.
What does the intersection point mean?
The intersection point is where two lines cross — the one place where both equations give the same y-value for the same x. That x-value is the solution to the equation, because it's the number that makes both sides equal.
Can every linear equation be solved graphically?
Yes! Any equation of the form ax + b = c can be solved by graphing y = ax + b and y = c. The lines always cross at exactly one point (as long as a ≠ 0), and the x-coordinate of that crossing is the solution.

Related Topics

Slope of a LineWhat is a Function?Introduction to Algebra