Two intercept form of a straight line

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:


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 $\frac{y-y_{1}}{y_{2}-y_{1}}=\frac{x-x_{1}}{x_{2}-x_{1}}$
Find m$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{2+5}{6+4}=\frac{7}{10}$ 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$y=mx+b$
$x=\frac{22}{10}\cdot \frac{10}{7}$
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:$\frac{-10y}{22}+\frac{7x}{22}=1$



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