Question

please help me. find the equation of a line through the points (2,8) and (1,5) in the form of x/a + y/b =1 where a and b are y and x intercepts

Answer 1

plug in your two points:

2/a + 8/b = 1
1/a + 5/b = 1

multiply the 2nd by 2 and you have

2/a + 8/b = 1
2/a + 10/b = 2

now subtract, and you have

2/b = 1
b = 2
use that to find that a=-2/3

x/(-2/3) + y/2 = 1

check the intercepts and you see that they are (-2/3,0) and (0,2)

Now you know why that's called the intercept form of the line.

Answer 2

The two-point form of a straigth line:

y - y1 = [ ( y2 - y1 ) / ( x2 - x1 ) ] · ( x - x1 )

In this case :

x1 = 2 , y1 = 8

x2 = 1 , y2 = 5

So:

y - y1 = [ ( y2 - y1 ) / ( x2 - x1 ) ] · ( x - x1 )

y - 8 = [ ( 5 - 8 ) / ( 1 - 2 ) ] · ( x - 2 )

y - 8 = [ ( - 3 ) / ( - 1 ) ] · ( x - 2 )

y - 8 = 3 · ( x - 2 )

y - 8 = 3 · x - 3 · 2

y - 8 = 3 x - 6

Add 8 to both sides

y - 8 + 8 = 3 x - 6 + 8

y = 3 x + 2


y = m · x + b

This is the "slope-intercept" form.

m is the slope

b is the y - intercept

In this case:

y - intercept = b = 2


Now you must find x - intercept

x - intercept is point where y = 0

y = 3 x + 2 = 0

3 x + 2 = 0

Subtract 2 to both sides

3 x + 2 - 2 = 0 - 2

3 x = - 2

Divide both sides by 3

x = - 2 / 3


x / a + y / b = 1

is the intercept form of the equation of a straigth line

a is the x - intercept

b is the y - intercept

In this case:

x - intercept = a = - 2 / 3

y - intercept = b = 2


x / a + y / b = 1

x / ( - 2 / 3 ) + y / 2 = 1

( x / 1 ) / ( - 2 / 3 ) + y / 2 = 1

( x · 3 ) / ( - 2 · 1 ) + y / 2 = 1

3 x / - 2 + y / 2 = 1

- 3 x / 2 + y / 2 = 1