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# Derive the intercept form or x/a+y/b=1 using the formulas of the slope.?

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The intercept form or x/a + y/b = 1 using the formulas of the slope

Formula: x/a + y/b = 1

i.e The line equation is the x - intercept a at point (a, 0) and the y - intercept b at point (0, b)

Recall: The slope formula is given for two points p(x₁, y₁) and q(x₂, y₂)

m =(y₂ - y₁) / (x₂-x₁ )

Now let x₁ = a, y₁ = 0, x₂ = 0, and y₂ = b substitute in the slope formula m = (y₂ - y₁) / (x₂-x₁ )

m = (b - 0) / (0 - a)

Simplify

m = b / (- a)

m = - b / a

Contuse .........

The y - intercept b at point (0, b) and slope is m then the line equation is  y = mx + b

where m = slope and b is y - intercept

But m = -b / a substitute above the line equation

The intercept form is y = (-b/a)x + b

y = (- bx + ab) / a           1, a LCM is a

Multiply each side by 'a'.

a(y) = [(- bx + ab) / a ] (a)

Simplify

ay = - bx + ab

ay + bx = - bx + ab + bx

bx + ay = ab

There fore The intercept form is bx + ay = ab
edited Jan 23, 2013
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slope-intercept form equation is y = mx + b where m is slope and b is y-intercept.

y-intercept is b. So, the line crosses the y-axis at (0, b).

Let the line crosses the x-axis at (a, 0).

Find the slope m =(y₂ - y₁) / (x₂-x₁ ).

Substitute the coordinate values in slope formula.

m = (b - 0) / (0 - a) = - b /a.

The line equation is y = (-b/a) x + b

Add (b/a) x to each side

(b/a) x + y = (-b/a) x + b + (b/a) x

(b/a) x + y = b

Divide the equation by b

x/a + y/b = 1

I hope it helps a lil.