Question

Which equation represents the line passing through the points (3, 2) and (-9, 6)?

Answer 1

Answer:

Step-by-step explanation:

The equation of a linear function in point-slope form is y – y1 = m(x – x1)

The point is A (x1 , y1)

in this exercice : x1 = 3  and  y1 =2

let  A(3,2)    B(-9,6)

the slope is : m =   (YB - YA)/(XB -XA)

(6-2)/(-9-3)  =4/(-12)  = -1/3

the slope is   m = -1/3

The equation is :  y – y1 = m(x – x1)

y-2 =-1/3 ( x-3)

or : 3y-6 = -x+3

Answer 2

The equation of the line that represents the line passing through the points (3, 2) and (-9, 6) is y=(1/-3)x+3.

What is the equation of a line?

The equation of line is given by,

y =mx + c

where,

x is the coordinate of the x-axis,

y is the coordinate of the y-axis,

m is the slope of the line, and

c is constant.

The slope of the line passing through the points is (3, 2) and (-9, 6) is,

$m=\dfrac{6-2}{-9-3} = \dfrac{4}{-12} =\dfrac{1}{-3}$

The general equation of a line is y=mx+c, now substitute any point in the equation to know the value of the constant c,

$y=mx+c\\\\2=\dfrac{1}{-3}(3)+c\\\\2=-1+c\\\\2+1=c\\\\c=3$

Hence, the equation of the line that represents the line passing through the points (3, 2) and (-9, 6) is y=(1/-3)x+3.

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