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

Answer:

second option

third option

fifth option.

Step-by-step explanation:

We have the slope of the line: $m=\frac{2}{3}$

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:

$y-2=\frac{2}{3} (x-1)$   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:

$y-4=\frac{2}{3}(x-4)$   which is the third option

finally, we can solve the previous equation for y:

$y=\frac{2}{3}(x-4)+4\\ \\y=\frac{2}{3}x-\frac{2}{3}(4)+4\\ \\y=\frac{2}{3}x-\frac{8}{3} +4\\\\y=\frac{2}{3}x+\frac{4}{3}$which is the fifth option.

Answer 2

Answer:

the answers are

Step-by-step explanation:

b.y – 2 = (x – 1)

c.y – 4 = (x – 4)

e.f(x)=2/3x+4/3