Overview Of Slope Point Form

What is a straight line equation?

The equation of a line seems to be calculated using the slope-intercept type of equation for a given straight line with coordinates. The slope-intercept formula requires the straight line’s slope value and the value of the intercept that forms because of the line’s intersection with the y-axis. A straight line equation seems to be a mathematical equation that expresses the relationship between different coordinates present on a straight line. It can be expressed in a variety of ways and indicates the line’s slope values, including the x-intercept as well as the y-intercept. The most popular expressions when representing straight line equations seem to be y = mx + c and ax + by = c.

Brief on slope point form or two-point of the straight-line equation

The two-point form seems to be one of the less common types of equations used while evaluating straight line equations. The point form equation helps in finding the result of a straight line if two coordinates points are known. The values of the coordinate points are then substituted in the place of the equation to help compute the answer. The formula for the two-point equation seems to be written in the form of y−y1 = (y2−y1/x2−x1) (x−x1). This seems to be a complex form of the equation when compared to other forms of the straight-line equation, but it is quite easy to solve, just like the other forms.

Here, x and y seem to be unknown values that need to be found, and the (x1,y1) and (x2,y2) seem to be coordinate values on the line.

Example

Question 1: The coordinate points with the value of A(3,4) b(2,3) form a straight line. Find its equation.

Solution:

It is asked to find the equation of the straight line. To find the answer one has to evaluate it in the two point form method, which is y−y1 = (y2−y1/x2−x1) (x−x1). The values need to be substituted in their respective places.

so,

Y-4 = 3-4/ 2-4 . X-3

Y-4 = -1/-2 . x-3

-2(y-4) = x-3

-2y + 8 = x-3

X+11+2y = 0 (answer)

The answer for the given line that passes through the coordinates A(3,4 B(2,3) seems to have the equation x+11+2y = 0.

Question 2: Find the y-intercept value when the value of A(2,-6) b(-4,8) forms a straight line. 

Solution:

It seems that the question requires the y intercept, so, to find the answer one has to evaluate it in the two point form method, which is y−y1 = (y2−y1/x2−x1) (x−x1). The values need to be substituted in their respective places.

so,

Y-(-6) = 8-(-6)/ -4-2 . X-2

Y+6 = 14/-6 . x-2

-6(y+6) = 14(x-2)

-6y – 36 = 14x-28

-6y = 14x + 8

Y = (-14/6)x + 8/6

It seems that the resultant equation has a similar form to the slope point intercept.

The y-intercept value is 8/6.

Question 3: The coordinate points with the value of A(4,5) b(3,4) form a straight line. Find its equation.

Solution:

It is asked to find the equation of the line that these two points lie on. To find the answer, one has to evaluate it in the two-point form method, which is y−y1 = (y2−y1/x2−x1) (x−x1). The values need to be substituted in their respective places.

so,

Y-5 = 4-5/ 3-5 . X-4

Y-5 = -1/-2 . x-4

-2(y-5) = x-4

-2y + 10 = x-4

X+14+2y = 0 (answer)

The answer for the given line that passes through the coordinates A(4,5) B(3,4) seems to have the equation x+14+2y = 0.

Conclusion

The article explains briefly slope 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 slope 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 = (y2−y1/x2−x1) (x−x1). The article also mentions a few terms related to the point form equation.