Which of the following line represents the equation of the line

3(x -2y) = 5x -12

Answer

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Step by Step Solution

Step 1

Looking at the equation below:

3(x -2y) = 5x -12

We know that this equation is not in the Slope-Intercept Form. Hence, we have to change it into the form of y=mx+b.

Step 2

To change the equation in the form of y=mx+b, we need to make y as the subject of the equation (i.e. y = something). Therefore:

Step 3

Now, from the given equation:

When we compare it with y = mx+b, we have:

slope = m = -1/3 y-intercept = b = +2 = 2

Step 4

Now, to draw the line, we need to look at the slope in more detail. Since the slope is defined by 'change in y' divide by 'change in x'. We can break down the the slope = -1/3 as shown below:

Step 5

With the following information,

y-intercept = 2 change in y = -1 change in x = 3

Only line B fits all these information as shown in the picture below: