Question

Which equation represents the graphed function?1. y=4x-22. y=-4x-23. y=1/4x-24. y=-1/4x-3

Answer 1

The general equation of a line is:

`y=m\cdot x+b`

Where m is the slope of the line and b its the value of the y-intercept of the line.

Q) The question asks about the equation of a graphed line.

A) In order to find the equation of the line, we note that it passes through the points:

`\begin{gathered} (x_1,y_1)=(0,-2) \\ (x_2,y_2)=(4,-1) \end{gathered}`

The first point give us the value of the y-intercept of the line (b), so the y-intercept is y = -2, and we have:

`b=-2`

Now we must calculate the slope (m) of the line. In general the slope of a line is given by the following formula:

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

Where (x1,y1) and (x2,y2) are the coordinates of two points of the line. Using the points of above and the last formula we find that:

`m=(y_2-y_1)/(x_2-x_1)=(-1-(-2))/(4-0)=(2-1)/(4)=(1)/(4)`

Answer

Using the values of m and b, and the general equation, we find that the equation of the line is:

`y=m\cdot x+b=(1)/(4)x-2`

Or: y = 1/4 x - 2

So the correct option is option number 3.