Slope-Intercept Practice

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Question 2

Which of the following line represents the equation of the line

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

slope-intercept form of a line


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Select and check your answer...

A. Line A
B. Line B
C. Line C
D. Line D

Step by Step Solution

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    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.

    slope-intercept form of a line
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    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:

    Changing the equation to Slope-Intercept Form
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    Step 3

    Now, from the given equation:

    The Slope-Intercept Form of 3(x-2y)=5x-12

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

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

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    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:

    • 'Change in y' = -1 and 'change in x' = 3
    • Slope is equals to 'change in y' divides by 'change in x'
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    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:

    Only Line B fits all the information
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    Step 6

    Clearly, the answer is B.