Slope Intercept Form

A straight line’s slope-intercept form is one of the most frequent ways to represent the equation of a line. The slope-intercept formula can be used to obtain the equation of a line when given the slope of a straight line and the y-intercept ( the y-coordinate of the point where the line intersects the y-axis). The equation of a line is the equation that each point on that line must satisfy. There are several ways to find this equation for a straight line.

Slope intercept form of a straight line

A method for determining the equation of a straight line in the coordinate plane is the slope-intercept form. The equation of a straight line is the following relationship:

1. Any point on the line’s coordinates must meet.

2. Any point not on the line’s coordinates will not satisfy.

It’s simple to figure out how to solve this equation. We’ll need the slope, or angle of inclination, of this straight line from the x-axis, as well as the intercept it makes with the y-axis, to get the slope-intercept form of a straight line.

Use the slope-intercept form of a straight line to find the equation of a line. The slope-intercept formula requires the line’s slope and the intercept cut by the line with the y-axis. Consider a straight line with the slope ’m’ and the y-intercept ‘b.’ Y = mx + b is the slope-intercept form equation for a straight line with a slope ’m,’ and ‘b’ as the y-intercept.

Slope Intercept form equation

In this section, you’ll learn how to deduce the slope-intercept form of a line’s equation.

Consider a line L with a slope of m that intersects the y-axis at c units from the origin.

The y-intercept of the given line L is defined as the distance c.

As a result, the coordinates of a point on the y-axis where the line L intersects will be (0, c).

That is, line L has a slope of m and passes through a fixed point (0, c).

The equation of a line in point-slope form, where the point is (x1, y1) and the slope is m, is:

(y – y₁) = m (x –x₁)

Here, (x₁, y₁ ) = (0, c)

We get by substituting these values:

y – c = m ( x- 0)

y – c = mx

y = mx + c

As a result, if and only if y = mx + c, the point (x, y) on the line with slope m and y-intercept c lies on the line.

Slope intercept form formula

The equation of the line in slope-intercept form, as derived above, is:

y = mx + c

Here,

(x, y) = every point on the line

m = slope of the line

c = y-intercept of the line

When utilizing the aforementioned formula, the variables x and y must usually be preserved as variables.

Slope intercept form x-intercept

The slope-intercept version of the equation for line L with slope m and x-intercept d can be written as:

y = m(x – d)

Here,

M is the line’s slope.

D is the line’s x-intercept.

Sometimes, the slope of a line may be stated in terms of tangent angle such as:

m = tanθ

Derivation of slope-intercept form standard form equation

From the equation of a straight line in standard form, we may get the slope-intercept form of the line equation:

As we all know, the conventional form of a straight line equation is:

Ax + By + C = 0

Rearrange the terms as follows:

By = – Ax – C

y = (-A/B)x + (-C/B)

The formula is y = mx + c.

The slope of the line is represented by (-A/B), while the y-intercept is represented by (-C/B).

Conclusion

Linear equations are used to model many real-world situations. We’ll look at a few examples here to show how equations written in slope-intercept form relate to real-world situations. Instead of x and y, different letters are usually used for the variables in a linear equation that models a real-world situation. The variable names help us remember what quantities we’re measuring.