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• y = mx + b – Definition, Slope-Intercept Form, Examples, Facts

y = mx + b – Definition, Slope-Intercept Form, Examples, Facts

Jessica Kaminski

reviewed by Jo-ann Caballes

Updated on March 10, 2026

The equation y = mx + b shows a straight line in what’s called slope-intercept form. Here, m is the slope, which tells you how steep the line is, and b is the y-intercept, or the point where the line crosses the y-axis. This equation lets you find the value of y for any value of x.

Here, we’ll cover the slope-intercept form y = mx + b, how to work out this equation, the y=mx+b meaning, and how to find the slope of the equation. 

What is y = mx + b?

y = mx + b is a formula that’s also known as the slope-intercept form of a linear equation. But what exactly does that mean?

If we take a straight line on a graph, we must recognize that it has certain properties, including: 

• The slope, which represents how steep the line is
• The y-intercept, which represents where the line crosses the vertical y-axis, i.e., how far up the line goes (b in slope-intercept form)
• The x-intercept, which represents where the line crosses the horizontal x-axis, i.e., how far along the line goes

What is m in y=mx+b?

In the equation y equals mx plus b, the letter m represents the slope of the line. The slope shows how steep the line is and how much y changes when x increases by 1. It is often described as “rise over run,” meaning how much the line rises or falls compared to how far it moves horizontally. A positive m means the line rises to the right, while a negative m means it falls.

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What is b in y=mx+b?

In the y=mx+b formula, the letter b represents the y-intercept. This is the point where the line crosses the y-axis. It shows you the value of y when x = 0. If you need to know how to find y mx b on a graph, you can find b by locating where the line touches the vertical axis.

What is x in y=mx+b?

In the y=mx+b slope, x represents any value along the x-axis (the horizontal axis). It is the input value you choose. When you substitute a number for x, the equation calculates the corresponding y value on the line.

What is y in y = mx + b?

In the equation, the letter y represents the output value that corresponds to a chosen x. It shows the position of a point on the line. For every value of x, the equation gives you a specific y, which helps you graph the line accurately.

y=mx+b example

Below, you can see that the slope goes 1 place across and 3 up, which means m = 3 ÷ 1. This means m = 3.

The line intercepts the y-axis at the +2 point, which means y = 2. 

Therefore, our slope-intercept form is y = 3x + 2.

In all y = mx + b equations, you’ll notice that the y and the x always remain as variables, while our m and b variables are replaced by numbers.

How to find y = mx + b?

Once we know our slope (represented by m) and our y-intercept (represented by b), we simply use these figures in our equation, replacing those two variables with our numbers. This is also how to graph a y=mx+b equation.

You’ll first need to calculate your slope, which is the rise (known as the vertical change) over the run (known as the horizontal change) between two points on a line. You’ll need to use the formula of m = rise ÷ run to find your slope. Then, once you know that number, you can replace m with it in your formula.

Then, you’ll need to find the point where the line crosses the y-axis. This must be the point where it crosses the axis at x = 0. Once we have these two values, whether by identifying them on our graph or by given data, we can replace the m and b in our equation. You won’t replace the variables of y or x with numbers.

y = mx + b at origin

You might be wondering how we calculate y = mx + b when our line passes through the origin in our graph – AKA the point of 0,0. 

In this case, in y=mx+b, what is b? Our y-intercept b becomes 0 because that’s where our line intersects the y-axis – at the point of 0. 

So, we can simplify the equation y = mx + b to y = mx.

This is a special case of the slope-intercept form because the line passes through the origin, which means b is 0.

How to find the y=mx+b slope?

To find the slope y = mx + b in your equation, you need to understand the difference in the x and y coordinates.

To work this out, you need to use the formula of m = rise ÷ run. This can also be expressed as m = (difference in y coordinates) ÷ (difference in x coordinates).

y = mx + b equations

There are some interesting facts you should know about y = mx + b equations that show how important they are to the world of mathematics and algebra. These facts and handy tips are:

• It’s the standard form used to describe any straight line in algebra
• When we talk about how steep a line is, we are referring to how steeply it rises or falls
• Positive slopes will move in an upward direction from left to right
• Negative slopes will move in a downward direction from right to left, meaning from left to right, they fall instead
• Lines with a zero slope or gradient are horizontal, with no rise or fall

Solved math tasks: examples

Now that you know everything there is to know about y = mx + b and how to use and solve it, try out our solved math tasks! Work them out for yourself, then check your answers to see how many you get right. You can always try again if you don’t get them quite right!

Solved math task 1

Let’s say you’re saving up for a new bicycle that costs $300. You already have $50, and each week you add $25 from your allowance to your savings. Express this as a linear equation.

Answer:

Here, the starting amount of $50 is your y-intercept (b).

The amount you save each week ($25) is your slope (m).

Therefore, if we let ‘x’ represent weeks and ‘y’ represent your total savings, the equation becomes y = 25x + 50.

Solved math task 2

Let’s imagine a company that sells cookies. It costs $100 to start up the business (buying ingredients, packaging, etc.) and each cookie costs $0.50 to make. Express this as a linear equation.

Answer:

The startup cost is the y-intercept (b = 100).

The cost per cookie is the slope (m = 0.5).

If ‘x’ represents the number of cookies and ‘y’ represents the total cost, our equation becomes y = 0.5x + 100.

y = mx + b: practice math problems

y=mx+b worksheets

Now that you know the y = mx + b meaning, it’s time to improve your knowledge of algebra, linear graphs, and the equation in practice.

Make sure to give a try to our fun, free math worksheets with engaging puzzles and games – as well as learning, you’ll have plenty of fun!

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Frequently asked questions on y = mx + b

How to find b in y=mx+b?

B represents the y-intercept, which is the point where the line crosses the y-axis. To find it, you need to look at the graph and identify where the line touches the y-axis. b is simply the constant number in your formula.

How to graph y=mx+b?

You need to start by plotting b on the y-axis. Then use the slope m, which shows the rise over run, to find the next points. You need to move up or down based on the slope, then left or right. Then, draw a straight line through the points.

What is the slope in y=mx+b?

In the equation, the slope is the number m. It tells you how steep the line is and how much y changes when x increases by 1. A positive slope rises to the right, while a negative slope falls.

Jessica Kaminski

91 articles

Jessica is a seasoned math tutor with over a decade of experience in the field. With a BSc and Master’s degree in Mathematics, she enjoys nurturing math geniuses, regardless of their age, grade, and skills. Apart from tutoring, Jessica blogs at Brighterly. She also has experience in child psychology, homeschooling and curriculum consultation for schools and EdTech websites.