All About Point Form Or Point-Slope Equation

Define a straight line equation?

The equation of a straight line can always be calculated using different types of equation formulas. The point-slope formula requires the straight line’s slope value as well as the values of the intercept that form because of the line’s intersection with the y-axis on a cartesian plane. This straight-line equation can be seen as a mathematical equation that represents the relationship between different values of coordinates that are present on a straight line. These equations have various forms and always seem to indicate the line’s slope values, including the x-intercept as well as the y-intercept. The most popular form of equation used when representing straight line equations seems to be y = mx + c and ax + by = c.

Brief on point form of a straight-line equation

The point-slope equation seems to be one of the major types of equation used while evaluating straight line equations. The point form equation helps in finding the result of a straight line with the help of a coordinate present on the straight line. The values of the coordinate points are then substituted in the place of the equation to help compute the answer. The equation needs various other factors as its variable if the answer is needed. One of these variables is called the slope of the straight line. One needs to find the slope if they want to find the answer for a straight-line equation. The slope can be evaluated in the following way.

• The slope of a line within the cartesian lane that has both the x-axis and y-axis seems to be defined in the form of a change in the y value of the coordinate by the change in the value of the x coordinate that is present on two different locations on a straight line. The slope is commonly denoted by the letter m. The following equation describes the slope of a straight line – m =  y2– y1/ x2– x1.

The formula for the point-slope equation seems to be written in the form of y – y1 = m(x  -x1)

Here, m seems to be the slope value that one needs to find if needed, and the x1y1 seem to be coordinate values, while x and y are unknown variables that one needs to find out.

Example: 

Question 1: A point on the cartesian plane represents the value of (24,8) and (16,4). Find the line’s equation.

Solution:

It seems that the question asks for an equation as its solution, so, taking into factor the coordinates and to find the answer, one has to evaluate it in point-slope form, which is y – y1 = m(x  -x1). The values need to be substituted in their respective places in the equation.

So,

M = 4-8/16-24 = -4/8 = -1/2

Now, putting the values in their places and later convert to a standard equation in the form ax + by = c

Y- 8 = -1/2(x – 24)

2y – 16 = -x + 24

2y = -x + 40

X + 2y = 40 (answer)

The answer for the straight line with coordinates A(24, 8) B(16,4) is x + 2y = 40.

Question 2:A point on the cartesian plane represents the value of (10,20) and (40,10). Find the line’s equation.

Solution:

An equation is asked as answer for the following coordinates,

So, slope is,

M = 10-20/40-10 = 10/30 = -1/3

Now, putting the values in their places,

Y- 20 = -1/3(x – 10)

3y – 60 = -x + 10

3y = -x + 70

X + 3y = 70 (answer)

The answer for the straight line with coordinates (10,20) and (40,10) is X + 3y = 70.

Question 3:A point on the cartesian plane represents the value of (12,30) and (24,16). Find the line’s equation.

Solution:

Step 1: Finding the slope

So,

M = 16-30/24-12 = -14/12 = -7/6

Now, put the values in their places, and converting to a standard equation

Y- 30 = -7/6(x – 12)

6y – 180 = -7x + 84

6y = -7x + 244

7X + 6y = 244 (answer)

The answer for the straight line with coordinates A(12,30) B(24,16) is7X + 6y = 244.

Conclusion

The article explains briefly point form and its definition; it further talks about what point form represents in mathematics as well as mentions some of its key concepts. A point seems to be a form of a linear equation that represents the mathematical equation of a straight line in the form of y – y1 = m(x  -x1). The article also mentions a few terms related to straight lines.