Question

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

Answer 1

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)

Answer 2

The slope-intercept form:

$y=mx+b$

m - slope

b - y-intercept

The formula of  slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

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

$m=\dfrac{-0.5-0.5}{3-(-3)}=\dfrac{-1}{6}=-\dfrac{1}{6}$

Put it to the equation of a line:

$y=-\dfrac{1}{6}x+b$

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

$-0.5=-\dfrac{1}{6}(3)+b$

$-0.5=-\dfrac{1}{2}+b$

$-0.5=-0.5+b$          add 0.5 to both sides

$b=0$

Answer: $\boxed{A.)\ y=-\dfrac{1}{6}x}$