Question

find the equation of a straight line,whose y- intercept is -4 and interacts the line2x+4y-12=0 at x- axis​

Answer 1

SOLUTION :

GIVEN

• A straight line whose y- intercept is - 4

• It intersects the line 2x + 4y-12 = 0 at x- axis

TO DETERMINE

The equation of the line

EVALUATION

Here for the straight line y- intercept is - 4

Let the equation of the line is

$\sf{ y = mx - 4\: } \: \: ......(1)$

Where m is the slope of the line

Now the line (1) intersects the line 2x + 4y-12 = 0 at x- axis

So For point of intersection we put y = 0 in 2x + 4y-12 = 0

So that

$\sf{2x - 12 = 0 \: }$

$\implies \sf{2x = 12 \: }$

$\implies \sf{x =6 \: }$

So the point of intersection is ( 6, 0)

Now the equation (1) passes through ( 6 , 0 )

So

$\sf{6 m - 4\: = 0}$

$\implies \displaystyle \sf{ m = \frac{4}{6} }$

$\implies \displaystyle \sf{ m = \frac{2}{3} }$

Hence the required equation of the line is

$\displaystyle \sf{ y = \frac{2}{3} x - 4}$

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