We need at least two points to determine the nature of a line. This analogy is used to quickly sketch a line if its equation is given in the Two Intercept-Form. Consider the following graph where a line L makes x-intercept at a and y-intercept at b on the axes. This means that L meets x-axis at the point (a, 0) and y-axis at the point (0, b).
Use the two-point form of the equation to substitute the values of the intercepts:
Again, a= x-intercept and b= y-intercept
To convert the equation into a slope-intercept form may y as the subject:
Example 1. Determine the equation of the line with x-intercept 4 and y-intercept 3.
x-intercept a = 4.
y-intercept b = 9.
Substitute in the formula as
Example 2. Find the equation of a straight line with X-intercept A(-7,0) and Y-intercept B(0,14).
From the above information, we know the X-intercept is a=-7 and the Y-intercept is b=14. Now we substitute the values in the formula of the intercepts form as given:
Example 3. Convert general form of the equation into intercept form for 9x-5y=4
Let x=0 find y-intercept:
Let y = 0 to find x-intercept:
Substitute the values in the two-intercept form:
Example 4. Reduce the general equation -8x+5y = 9 into intercept form and find the x-intercept and y-intercept.
First, divide both sides by 9
Now bring the x and y coefficient to the denominator:
From the equation above, the x-intercept is -9/8 and y-intercept is 9/5.
Example 5. Find the x- and y-intercepts of the line using these coordinates, (–4, –5) and (6, 2).
Convert the points to intercept form equation by:
|Using slope-intercept form||Using two-point form|
|y = mx + b|
|Find m||Substitute the values of an ordered pair to form general equation:|
|Substitute (6, 2 ) in the slope-intercept form to obtain y-intercept:|
b = -22/10
|Convert the general equation into intercept form:|
|Substitute m and b to find x intercept when y=0|
a = -22/7
|Shift the coefficient of x and y to the denominators:|
a=22/7 and b=-22/10
|Substitute the values of a and b in the intercept form:||The equation is written as:|