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What is the equation of a line that passes through points (-3,0.5) and (3, -0.5)?

A.) y = -1/6x
B.) y = -6x
C.) y = -1/6x + 1
D.) y = -6x - 17.5

Respuesta :

Answer:

y=-1/6x + 0   or     y=-1/6x    (when b = 0 then you leave it out)

Step-by-step explanation:

Find the slope:

-0.5 - 0.5/3 - (-3) = -1/6

Find the y intercept (b): Plug in the x, y and m into y= mx + b

0.5=(-3)(-1/6) + b

0.5=1/2 + b

0.5-0.5 = b (change the 1/2 into a decimal 0.5 to make it easier to subtract

0=b

Now plug in the m and the b that you just found into the equation y=mx+b

y=-1/6x + 0 or y=-1/6x    (when b = 0 then you leave it out)

gmany

The slope-intercept form:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

The formula of  slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points (-3, 0.5) and (3, -0.5). Substitute:

[tex]m=\dfrac{-0.5-0.5}{3-(-3)}=\dfrac{-1}{6}=-\dfrac{1}{6}[/tex]

Put it to the equation of a line:

[tex]y=-\dfrac{1}{6}x+b[/tex]

Put the coordinates of the point (3, -0.5) to the equation of a line:

[tex]-0.5=-\dfrac{1}{6}(3)+b[/tex]

[tex]-0.5=-\dfrac{1}{2}+b[/tex]

[tex]-0.5=-0.5+b[/tex]          add 0.5 to both sides

[tex]b=0[/tex]

Answer: [tex]\boxed{A.)\ y=-\dfrac{1}{6}x}[/tex]

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