All about Intercept Form

What is a straight line equation?

The straight line’s general mathematical equation can be represented in the form of y = mx + c, where the letter m seems to be the line’s slope while c seems to be the value for the y-intercept. In geometry, it seems to be the most frequent type of the equation when a straight line seems to be in question. A straight line’s mathematical equation can be represented in a variety of ways, and these types are called point-slope, slope-intercept, general, standard and a few others. A straight line seems to be a geometrical construct that seems to have one dimension that continues till infinity on all of its ends.

Brief on Intercept form of a straight-line equation

A mathematical equation in the form of x/a + y/b = 1 seems to be the intercept representation of a straight line. This seems to be one of the most common types of equations a straight line represents. The way these intercepts are represented with the help of symbols in a line equation also assists in determining the line’s position in relation to coordinate points located throughout axes. The intercept type of equation used inline equations could also be thought of as a line that forms a type of right triangle with the help of coordinate axes values, and the sides of the triangles’ lengths seem to be represented with ‘a’ and ‘b’ units, respectively.

The x-intercept seems to be the smallest distance between the origin and a point that seems to be on the x-axis where the line intercepts it, and even the y-intercept value seems to be the shortest route between the origin as well as a point present on the y-axis where the line intersects it.

The variables throughout the equation seem to be represented with x and y, including the x- and y-intercepts which are represented by a and b, respectively. The slope of this equation seems to be represented by -b/a.

As this line seems to intersect both of the coordinates on a cartesian plane, it seems to form a right triangle, and the area regarding this right-angled triangle seems to be equal to that of the product and of half of the triangle’s intercepts. Furthermore, these intercept forms can always be converted into a simple form as ax + by = c, which seems to be the standard form when representing a straight line’s equation.

Example

Question 1: The axes with the value of 4x – 6y – 60 = 0 forms a triangle. Find its area.

Solution:

The question asks for the area of the triangle with the help of the given equation. To find the answer, it’s important to convert the equation into the intercept form.

4x – 6y = 60

(4x – 6y)/50 = 1

4x/60 + 6y/60 = 1

x/15 + y/10 = 1

It can be seen that the resultant equation forms an x/a + y/b = 1 type of form that seems to represent the intercept form. The a seems to be 15, and the b seems to be 10 in this case.

1/2 x ab seems to be the area of the triangle that is formed with the help of these coordinate points with the value of 4x – 6y -60 = 0.

Area of the given triangle = 1/2 x (15 x 10) = 75 (answer).

Question 2:

Find the intercepts of the given question with an equation of 15x + 5y – 45 = 0 as its variables.

Solution:

In this question it seems that the intercept points are asked so we need to first convert the equation.

15x + 5y = 45

(15x + 5y)/45 = 1

15x/45 + 5y/45 = 1

x/3 + y/9 = 1

When compared to the intercept form of the equation, the x-intercepts seem to be 3, and the y-intercept seems to be 9.

Conclusion

The article explains briefly about intercept form and its definition; it further talks about what intercept form represents in mathematics as well as mentions some of its key concepts. An intercept seems to be a form of a linear equation that represents the mathematical equation of a straight line. The article also mentions a few terms related to intercept form equations.