Question

Which equation represents the graphed function?54-3x + 2 = y321Ox+ 2 = yo x-3=y1/2 3 4 5 X5 4 3 2 1-22x - 3 = yเจ

Answer 1

In the present problem, we can see the graph goes through the following points: (2, 0) and (0, -3)

To solve the question, we can do both: Or substitute the values into the possible answers and see if it fits, or use it to find the equation of the line.

We are going to use the second.

We know that the equation of a line is given by:

`y(x)=ax+b`

Where, for any two points P₁(x₁,y₁) and P₂(x₂,y₂) that the line goes through, we can use it to find the constants a and b as it follows:

`\begin{gathered} a=(y_2-y_1)/(x_2-x_1) \\ b=y(0)_{} \end{gathered}`

Once we have P₁(2, 0) and P₂(0, -3), we can substitute it:

`\begin{gathered} a=(-3-0)/(0-2)=(3)/(2) \\ b=y(x_2)=y_2=-3 \end{gathered}`

From this, we can write the equation of the line:

`y=(3)/(2)x-3`

From this, the answer is C)