Math Question. Should be Easy, but I'm lost.?

Question

Show that the line with intercepts (a, 0) and (0, b) has the following equation:

x/a + y/b = 1, a can NOT = 0, b can NOT = 0.

Please explain how you got your answers.
Thanks.

Answer 1

Slope of any line passing through (x, y) and (x', y') is
m = (y - y')/(x - x')

Hence, slope of line through (a, 0) and (0, b) is
m = (0 - b)/(a - 0) = - b/a

Equation of a line passing through (x', y') having slope m is given by
y - y' = m (x - x')

So, the equation of line through (a, 0) having slope m = - b/a is

y - 0 = - (b/a) ( x - a )

Rearranging, x/a + y/b = 1.

Answer 2

To show that a given point is on the graph, you only need to put the values into the equation and see if you get a true statement. Remember, the line is simply all of points that satisfy the equation.

For (a,0) put a in for x and 0 in for y:
(a)/a + (0)/b = 1 since (a)/a = 1 and (0)/b = 0, then:
1 + 0 = 1
1 = 1 since this is true, (a,0) will be on the line

For (0,b) put 0 in for x and b in for y:
(0)/a + (b)/b = 1 since (0)/a = 0 and (b)/b = 1, then:
0 + 1 = 1
1 = 1 since this is true, (0,b) will be on the line

If they asked, "Is the point (-a,0) on the line?" you would follow the same steps, but end up with a false statement. That means the given point is not on the line.

For (-a,0) put -a in for x and 0 in for y:
(-a)/a + (0)/b = 1 since (-a)/a = -1 and (0)/b = 0, then:
-1 + 0 = 1
-1 = 1 since this is false, (-a,0) will not be on the line

Answer 3

m = b / (- a) = ( - b / a )
Line passes thro` ( a, 0 )
y - 0 = (- b / a) ( x - a )
a y = - b x + a b
y = - ( b / a ) x + b
( 1 / b ) y = - ( 1 / a ) x + 1
x / a + y / b = 1

Answer 4

ur Q is

Show that the line with intercepts (a, 0) and (0, b) has the following equation:

x/a + y/b = 1, a can NOT = 0, b can NOT = 0.
.........................................................................................................

ans

consider the eq of a line lx+ny=d

satisfy these points in line

la+n*0=d

0*l+nb=d so l=d/a and n=d/b

put these subtitution in eq

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

d cancels

so x/a+y/b=1

Answer 5

The equation given is ni intercept form.

In problem they have given two points on line (a,0) and (0,b)
Here you can use two point form
It states
(X-X1)/(X1-X2)=(Y-Y1)/(Y1-Y2)
i.e.(X-a)/(a-0)=(Y-0)/(0-b)
i.e.(X-a)/a=Y/(-b)
I.e.X/a-1=-Y/b
ie X/a+Y/b=1

Answer 6

x/a+y/b=1
when y=0,
x/a+0/b=1
x/a=1
x=a, so (a,0)

x/a+y/b=1
when x=0
0/a+y/b=1
y=b
so (0,b)