Question

The slope of the graphed line is 2/3. Which formulas

represent the line that is graphed? Check all that apply.
y-1=2/3(x - 2)
y - 2=2/3(x - 1)
y-4 =2/3(x – 4)
F(x) =2/3x+1/3
f(x) = 2/3x+4/3

Answer 1

Heya! Your answers are B,C,E

Explanation:

You're welcome guys

Answer 2

second option

third option

fifth option.

Explanation:

We have the slope of the line:
`m=(2)/(3)`

and we can see that the line passes through the points (1, 2) and (4, 4)

We can use the point slope equation:

`y-y_(0)=m(x-x_o)`

first, we use the first point (1, 2) and we define
`x_0=1` and
`y_0=2`. Substituting these values along with the value of the slope:

`y-2=(2)/(3) (x-1)` which is the second option

Now, using the second point (4, 4) and defining
`x_0=4` and
`y_0=4`, using again the point slope equation
`y-y_(0)=m(x-x_o)`, we get:

`y-4=(2)/(3)(x-4)` which is the third option

finally, we can solve the previous equation for y:

`y=(2)/(3)(x-4)+4\\ \\y=(2)/(3)x-(2)/(3)(4)+4\\ \\y=(2)/(3)x-(8)/(3) +4\\\\y=(2)/(3)x+(4)/(3)`which is the fifth option.