![]() If you know two points on the line, you can use the slope formula above to find it or use a slope calculator. The first step is to find the line’s slope. You can express the equation of a straight line in slope-intercept form in a few steps. Then, since point (x 2, y 2) is an arbitrary point on the line, we can rename it to just (x, y).įinally, we see that the resulting equation of the line is the slope-intercept form equation above. Now, we can substitute the y-intercept (which, by definition, is the coordinate (0, b)) for (x 1, y 1). If you multiply both sides of this equation by the denominator (x 2 – x 1), the formula can be rewritten as: The formula for slope using the coordinates for two points (x 1, y 1) and (x 2, y 2) is: Slope-intercept form is derived from the slope formula. In the slope-intercept formula, the slope of the line m is the coefficient for the x-coordinate, and the y-intercept is represented as the b variable. The slope-intercept form of a line states that the y-coordinate y of a point on the line is equal to the slope m times the x-coordinate x plus the y-intercept b. The slope-intercept form equation is given by: The y-intercept is the y-coordinate where the line crosses the y-axis. Slope-intercept form is applicable when you have the slope and y-intercept for a line or when you can calculate these for the line. The combination of these elements can be used to plot any point on the line. Slope-intercept form gets its name because the equation contains the slope and the y-intercept of the line. The slope-intercept form equation can be used to find any point on the line. Slope-intercept form is a type of linear equation format used to express a straight line. Slope-intercept form is probably the most frequently used equation format to represent a line, but you can also express the line in point-slope form or standard form. ![]() You can use a calculator like the one above to find the equation for a straight line in slope-intercept form, but you can also follow the steps below to find it. The most commonly used method is an algebraic equation in slope-intercept form. You can continue your study with the following lessons.There are several ways to describe a line using its slope, or gradient. Understanding the equation of a line is one part of the overall study of linear equations and their graphs. Continue your study of linear equations and graphing This means that we just need to bring the x-term to the other side. This is the easiest case, because the coefficients on x and y are already integers (negative or positive whole numbers). Write the equation of the line in standard form: We will now look at some examples of writing the standard form of a line, when the line is already given in y = mx + b form.įirst, let’s start with one where there aren’t many steps needed. We will follow these rules in this lesson. It is also common to require that A, B, and C share no common factors. While they technically can be any real numbers, it is most common to write them as integers and to keep A positive. Note that the requirements on A, B, and C vary a bit from textbook to textbook. As you will see in the lesson below, every line can be expressed in this form. ![]() The standard form is just another way to write this equation, and is defined as Ax + By = C, where A, B, and C are real numbers, and A and B are both not zero (see note below about other requirements). You are probably already familiar with the slope-intercept form of a line, y = mx + b. The standard form of a line is simply a special way of writing the equation of a line.
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