In the general terms, the slope intercept form assumes the formula y = mx + b wherein:
M is considered to be the slope and b is considered to be the y intercept wherein the line begins. The intercept form of the line is defined as if a and b are non-zero X and Y intercepts of line I, then the respective equation which will be forming is xa + yb=1. Since, a is considered the X intercept of line I and any point which lies on x axis its value of the Y is equal to zero and it passes through the point A (a,0).
For instance- y=5x + 3, it is considered to be the example of Slope Intercept Form and it helps in representing the equation of line with slope of 5 and a y-intercept of 3.
The other instances of the Intercept include the following:
A line intersects X-axis and Y-axis at point A and B respectively. It passes through the point C (4,3) which helps in dividing AB in ratio 1:2 internally. Find the equation of the respective line.
The two conditions which are required to be analyzed are:
(i) passes through a particular point
(ii) point that helps in dividing AB in the ratio 1:2
In the respective scenario, we require to assume the equation of the line and convert the same in the equations which are needed to be solved.
The first condition is straightforward and whatever, the equation which have been assumed, the points coordinates are required to be substituted for x and y in the respective equation. For the second equation:
Equation of the line= x/a + y/b=1, in the respective scenario, coordinates A and B will be easy to analyse and the application is done as follows:
4 = 2 × a+1× 0/2 + 1 wherein it will be giving a=6
And, similarly, 3= 2*0 + 1*b/2 + 1 wherein it gives b= 9 and the required equation is as follows:
x/6 + y/9 = 1
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