Question

What is the equation of the following line? Be sure to scroll down first to see all answer options.

A.
y = 3x

B.
y = -3x

C.
y = 2x

D.
y = 6x

E.
y = 1/3x

F.
y = - 1/3x

Answer 1

y=1/3x

Explanation:

change in y/ change in x

2-0/6-0= 2/6=1/3

since its a positive slope, it’s 1/3

Answer 2

E.
`y=(1)/(3)x`

Explanation:

Take the two points shown:

`(0,0)(6,2)`

Use these to make an equation in slope-intercept form:

`y=mx+b`

m is the slope and b is the y-intercept (where x is equal to 0).

Use the slope formula:

`(y_(2)-y_(1))/(x_(2)-x_(1)) =(rise)/(run)`

Rise over run is the change in the y-axis over the change in the x-axis, otherwise known as the slope. Insert coordinate points:

`(0_(x1),0_(y1))\\\\(6_(x2),2_(y2))\\\\(2-0)/(6-0)`

Simplify:

`(2-0)/(6-0) =(2)/(6) =(1)/(3)`

The slope is
`(1)/(3)`. Insert this into the equation:

`y=(1)/(3)x+b`

Now find the y-intercept. Take one of the coordinate points and insert:

`(6_(x),2_(y))\\\\2=(1)/(3)(6)+b`

Solve for b. Simplify multiplication:

`(1)/(3)*(6)/(1)=(6)/(3)=2\\\\ 2=2+b`

Use reverse operations to isolate the variable:

`2-2=2-2+b\\\\0=b`

The y-intercept is equal to 0. Insert this into the equation:

`y=(1)/(3)x+0`

or

`y=(1)/(3)x`

:Done