Question

Graph of the linear equation ax + by + c = 0 a is not equal to 0 cuts x axis and y axis respectively at the point

Answer 1

Given:

Linear equation is:

$ax + by + c = 0$

The graph of linear equation will cut the x axis at a point where value of y coordinate will be 0.

i.e. we can let the point (p,0). This point will be on x axis because value of y axis is 0.

So, let us put the following values:

$x = p\\y = 0$

in the linear equation $ax + by + c = 0$.

$a\times p + b\times 0 + c = 0\\\Rightarrow ap+c =0\\\Rightarrow ap =-c\\\Rightarrow p = -\dfrac{c}{a}$

i.e. the point where the graph of linear equation $ax + by + c = 0$ cuts the x axis is:

$(-\dfrac{c}{a},0)$

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The graph of linear equation will cut the y axis at a point where value of x coordinate will be 0.

i.e. we can let the point (0,q). This point will be on y axis because value of x axis is 0.

So, let us put the following values:

$x = 0\\y = q$

in the linear equation $ax + by + c = 0$.

$a\times 0 + b\times q + c = 0\\\Rightarrow bq+c =0\\\Rightarrow bq =-c\\\Rightarrow q = -\dfrac{c}{b}$

i.e. the point where the graph of linear equation $ax + by + c = 0$ cuts the y axis is:

$(0-\dfrac{c}{b})$

Answer 2

(0-c/b) this is your answer