Question

If a is the x-intercept, b is the y-intercept, and m is the slope of the line with equation x/4+y/12=1, then what is the value of a+b+m?

Answer 1

Answer:

the required answer is 13

Answer 2

If x- intercept of line is a and y-intercept is b then double intercept form of equation of line :-

$\rm \dfrac{x}{a} + \dfrac{y}{b} = 1.......(1)$

But equation of line is given as :-

$\rm \dfrac{x}{4} + \dfrac{y}{12} = 1.......(2)$

Now, by comparing (1) and (2) , we get :-

a = 4 and b = 12

Now , we will convert equation (2) into slope intercept form of equation of line in order to find out slope of line.

$\rm \longrightarrow \dfrac{x}{4} + \dfrac{y}{12} = 1 \\ \\ \rm \longrightarrow \dfrac{3x + y}{12} = 1\\ \\ \rm \longrightarrow 3x + y= 12\\ \\ \rm \longrightarrow y= - 3x + 12$

slope of line = -3

m = -3

We have to find out the value of a+b+m.

=> a+b+m

=> 4+12-3

=> 4+12-3

=> 16-3

=> 13

Answer : 13

Additional Information :

$\rm \: Equation \: of \: line \: passing \: through \: points \: (x_1 , y_1) \: and \: (x_2 , y_2) :$

$\tt \longrightarrow y - y_1 = x-x_1\bigg( \dfrac{y_2-y_1}{ x_2-x_1} \bigg )$

$\tt \rightarrow \: here \: \bigg( \dfrac{y_2-y_1}{ x_2-x_1} \bigg ) is \: slope \: of \: line$