What is the equation of the line shown?

2x-y-3=0

Step-by-step explanation:

Here the line crosses the y -axis at −3 , so the y -intercept is −3 .  

Here the line crosses the x -axis at 1.5 , so the x -intercept is 1.5 .

If x=0, then y= -3 because

-y-3=0

-y=3

y= -3

If y=0, then x=1.5 because

2x-3=0

2x=3

x=1.5

The answer is:

The third option,

From the graphic we know that we are looking for a function that cut the x-axis at 2.5 and the y-axis at -3, also, the function has an increasing slope.

So, which function can meet all the mentioned before?

Let's try with each given equation and discard:

- First function:

Finding the x-axis intercept by making y equal to 0, we have:

Now, making "x" equal to 0, to find the y-axis intercept, we have:

So, for the first function we have that it has a positive slope and the intercepts with the x-axis(3,0) and the y-axis (0,-1.5), hence, this function does not match with the given graph.

- Second function:

Finding the x-axis intercept by making y equal to 0, we have:

Now, making "x" equal to 0, to find the y-axis intercept, we have:

So, for the second function we have that it has a negative slope and the intercepts with the x-axis(-1.5,0) and the y-axis (0,3), hence, this function does not match with the given graph.

- Third function:

Finding the x-axis intercept by making y equal to 0, we have:

Now, making "x" equal to 0, to find the y-axis intercept, we have:

So, for the third function we have that it has a positive slope and the intercepts with the x-axis(1.5,0) and the y-axis (0,-3), hence, this function matchs with the given graph.

Hence, the answer is:

The third option,

Have a nice day!