Linear equation facts for kids

The linear equations of y=-x+5 and y=.5x+2. The x's are variables.

In mathematics, a linear equation is a special kind of equation. It's called "linear" because when you draw it on a graph, it always makes a straight line. Think of it like drawing a path that never bends or curves!

Linear equations usually look like this:

y = mx + b

or sometimes like this:

(y - y1) = m(x - x1)

These equations help us understand how two things are related in a simple, straight-line way.

What are the Parts of a Linear Equation?

Let's break down the most common form, y = mx + b, to see what each part means.

Understanding 'm' (The Slope)

The letter m stands for the slope of the line. The slope tells you how steep the line is and which way it's going.

• If m is a big number, the line will be very steep.
• If m is a small number, the line will be flatter.

The slope also tells you the direction:

• If m is a positive number (like 2 or 0.5), the line goes up as you read it from left to right. It's like walking uphill!
• If m is a negative number (like -3 or -1.2), the line goes down as you read it from left to right. It's like walking downhill!

Understanding 'b' (The Y-Intercept)

The letter b stands for the y-intercept. This is a very important point on your graph.

• The y-intercept is the exact spot where your straight line crosses the vertical line on the graph, which is called the y-axis.
• It tells you the value of 'y' when 'x' is zero.

What are 'x' and 'y'?

• x and y are called variables. This means their values can change.
• When you graph a linear equation, 'x' usually represents the horizontal position (left or right), and 'y' represents the vertical position (up or down).
• For every 'x' value you pick, the equation will tell you the 'y' value that goes with it, creating a point on your straight line.

Different Forms of Linear Equations

There are a couple of common ways to write linear equations, each useful for different things.

Slope-Intercept Form

The equation y = mx + b is called the slope-intercept form.

• It's super handy because you can easily see the slope (m) and the y-intercept (b) just by looking at the equation.
• This form is great for quickly sketching a line on a graph.

Point-Slope Form

The equation (y - y1) = m(x - x1) is called the point-slope form.

• In this form, 'm' is still the slope.
• '(x1, y1)' is a specific point that the line goes through.
• This form is useful if you know the slope of a line and one point it passes through, but you don't know the y-intercept yet.

Why are Linear Equations Important?

Linear equations are used all the time in real life! They help us:

• Predict things, like how much money you might earn over time if you get paid the same amount per hour.
• Understand relationships, like how the distance you travel changes with time if you're moving at a steady speed.
• Solve problems in science, engineering, and even everyday budgeting.

See also

In Spanish: Ecuación de primer grado para niños