Question

What's the answer ? (Picture above) ​

Answer 1

Answer :

1st Option : y = -¾•x - 3

Note :

• The slope y-intercept form of a line is given by ; y = mx + c , where m and c are the slope and y-intercept respectively .
• The slope of a straight line is given by ; m = ∆y/∆x .

Solution :

★ Method 1 :

Here ,

It is given that , the slope of required line is -¾ , ie. m = -¾ .

Now ,

The slope y-intercept form of the required line will be given as ;

=> y = mx + c

=> y = -¾•x + c -------(1)

Also ,

It is given that , the required line pass through the point (4 , -6) , thus the coordinates of the point (4 , -6) must satisfy the eq-(1) .

Thus ,

Putting x = 4 and y = -6 in eq-(1) , we get ;

=> -6 = -¾•4 + c

=> -6 = -3 + c

=> c = -6 + 3

=> c = -3

Now ,

Putting c = -3 in eq-(1) , we will get the required equation as ;

=> y = -¾•x + c

=> y = -¾•x + (-3)

=> y = -¾•x - 3 (1st Option)

★ Method 2 :

Here ,

It is given that , the slope of required line is -¾ , ie. m = -¾ .

Also ,

We know that , the slope of a straight line is given by ; m = ∆y/∆x

→ m = (y - ß)/(x - α) ------(1)

where (α,ß) is a point through which the line passes .

Here ,

It is given that , the required line passes through the point (4,-6) , ie. (α,ß) = (4,-6) .

Now ,

Putting m = -¾ , α = 4 and ß = -6 in eq-(1) , we will get the required equation as ;

=> m = (y - ß)/(x - α)

=> -¾ = [y - (-6)]/(x - 4)

=> -¾ = (y + 6)/(x - 4)

=> -¾•(x - 4) = y + 6

=> -¾•x + ¾•4 = y + 6

=> -¾•x + 3 = y + 6

=> -¾•x + 3 - 6 = y

=> -¾•x - 3 = y

=> y = -¾•x - 3 (1st Option)