Question

the answer choices area. y = 1/3x +2b. y = 2x + 1/3c. y = -1/3x. + 2d. y = -2x - 1/3

Answer 1

We have to find the line equation of the function shown. We see that passes through the points:

`(0,2)\text{ and }(3,1)`

For doing so, we will find the slope and the y-intercept. The slope is given by the expression:

`m=(y_2-y_1)/(x_2-x_1)`

where (x₁,y₁) and (x₂,y₂) are two points of the line. In this case, replacing we obtain:

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

And thus, the slope is - 1/3. Now, for the y-intercept, we remember that when the x-coordinate is 0, the y-intercept is the y-coordinate.

As the line passes through the point (0,2), the y-intercept will be 2.

Putting those two together, the equation of the line will be:

`\begin{gathered} y=mx+b \\ y=-(1)/(3)x+2 \end{gathered}`