Show that an eq. with line x-intercept a and y-intercept b is x/a + y/b = 1. Called intercept form????????????

Question

Show that an equation of the line having x-intercept a and y-intercept b is x/a + y/b = 1. This is called intercept form.

How do I do this? Please help and be clear in all steps. Thanks in advance

Answer 1

Equation of a straight line --> y - y1 = m(x - x1)
where m is the gradient and (x1, y1) is a point that lies on the line.

Gradient of a straight line --> (y2 - y1)/(x2 - x1)
where (x1, y1) and (x2, y2) are two different points that lie on the line.

Given: x intercept a and y-interecept b
which means that the line consists of these two coordinates
(a, 0) and (0, b).

Gradient of line --> (b - 0)/(0 - a) = - b/a

Applying equation of line,
y - 0 = (- b/a)(x - a)
y = (- b/a)x + b
Multiplying by b throughout......
y/b + x/a = 1

Therefore, the equation of a straight line with x-intercept a and y-intercept b can be expressed as x/a + y/b = 1.
(Shown)

Answer 2

Actually, amazingly easy. Just sketch an x,y surface with the 2 intercepts (for convenience, let them both be positive). You can show that the slope-intercept format is y = - (b/a) x +b
Take the equation you have, multiply both sides by b and rearrange to the slope intercept form. It will be identical.

Answer 3

in the intercept type, the value 'a' is the x-intercept, which became into given to you as 3. further, the value 'b' is the y-intercept, which became into given as -2. Then the equation of the line is x/3 - y/2 = a million

Answer 4

(a,0) and (0,b) are the two intercepts.
y - b = [b/(-a)]x, point-slope form
Collect variables in the left side and constant in the right side, and divide each term by b,
bx/a + y = b
x/a + y/b = 1.

Answer 5

if you are given in the slope intercept form
y=mx+B
y=m(x+B/m)
y/m-x=B/m
multiply both sides by m/B
m/B* (y/m)-m/b(x)=1
y/B-x/(b/m)=1
on the otherhand if given in standard form
Ax+By=C
Ax/C+By/C=1
x/(C/A)+y/(c/B)=1