Calculate Slope Intercept Form from Two Points

When given two points on a line, you can use them to calculate the slope-intercept form of the line. This equation is written as y = mx + b, where m is the slope and b is the y-intercept.

For example, let's say we have a line with a slope of 1/2 and a point (5, 6). To find the equation in slope-intercept form, follow these steps:

Step One: Identify the slope and y-intercept. In this case, the slope is 1/2 and there is no given y-intercept.

Step Two: Use the slope formula to calculate the slope. If you know two points on the line, you can use the formula (y2 - y1) / (x2 - x1) = m, where m is the slope.

Step Three: Express the line in slope-intercept form. You can do this by plugging in the slope and y-intercept into the equation y = mx + b.

In this case, since we know the slope is 1/2 and there is no given y-intercept, we can use a y-intercept calculator to find it. Alternatively, you can input the slope and coordinates for a known point on the line for the m, x, and y variables in the equation y = mx + b.

If you know the slope already, then you can skip this step. However, 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 (x2, y2) is an arbitrary point on the line, we can rename it to just (x, y).

Finally, 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 (x1, y1).

If you multiply both sides of this equation by the denominator (x2 - x1), the formula can be rewritten as:

m = (y2 - y1) / (x2 - x1)

The formula for slope using the coordinates for two points (x1, y1) and (x2, y2) is:

Slope-Intercept Form

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:

y = mx + b

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. There are several ways to describe a line using its slope, or gradient.

Calculate slope intercept form from two points