In the xy-plane, what is the slope of the line whose equation is

In the $xy$-plane, what is the slope of the line whose equation is $3x-2y=8$ ?

  1. $-4$
  2. $-8/3$
  3. $2/3$
  4. $3/2$
  5. $2$

So, you were trying to be a good test taker and practice for the GRE with PowerPrep online. Buuuut then you had some questions about the quant section—specifically question 10 of Section 4 of Practice Test 1. Those questions testing our knowledge about Coordinate Geometry can be kind of tricky, but never fear, PrepScholar has got your back!

Survey the Question

Let’s search the problem for clues as to what it will be testing, as this will help shift our minds to think about what type of math knowledge we’ll use to solve this question. Pay attention to any words that sound math-specific and anything special about what the numbers look like, and mark them on your paper.

We are asked about the slope of a line equation, which tells us that we will use our Coordinate Geometry math skill. Let’s try to remember what we’ve learned about this skill as we approach this question.

What Do We Know?

Let’s carefully read through the question and make a list of the things that we know.

 

  1. We are given a line equation with $x$ and $y$
  2. The equation is located in the $xy$-plane
  3. We want to know the slope of the line equation

 

Develop a Plan

We see that we have the equation of a line and want to know its slope. From our Coordinate Geometry lessons,
we know that the slope of a line is easy to find if we put the line in slope-intercept form:

$$y=m·x+b$$

Here, the $m$ represents the slope of the line, and we can see that it is the number multiplied by $x$. We need our equation to mirror this one, looking as similar to it as possible. That means the $y$ must be by itself on the left side of the equation. So let’s plan to solve our equation for $y$, then we’ll know that the slope is whatever number is multiplied by $x$.

Solve the Question

Let start by writing our line equation on our paper, then we’ll put it into slope-intercept form to find the slope.

$$3x-2y=8$$

We know that for solving for a variable in an equation, we need to use the order of operations backwards (PEMDAS = Parentheses, Exponents, Multiplication, Division, Addition, Subtraction). Looking at using addition or subtraction to isolate the $y$, let’s move the 3x term to the right side by subtracting 3x from both sides of the equation:

$3x-2y$ $=$ $8$
$-3x$ $=$ $-3x$
$-2y$ $=$ $-3x+8$

Looks like that’s all of the addition and subtraction that we can do to isolate the $y$. Next, looking at multiplication and division, since the $y$ is multiplied by $-2$, let’s finish isolating the $y$ by dividing both sides by $-2$.

$-2y$ $=$ $-3x+8$
${-2y}/{-2}$ $=$ ${-3x+8}/{-2}$
${-2y}/{-2}$ $=$ ${-3x}/{-2}+8/{-2}$
$y$ $=$ $3/2·x-4$

Now that our equation is in slope-intercept form, we can see that the slope, which is the number multiplied by the $x$ in the equation, is $3/2$ for this line.

The correct answer is D, $3/2$.

What Did We Learn

Slope is a commonly tested math principle on the GRE. It’s definitely easiest to recognize as the $m$ in the slope-intercept form of the equation, so let’s commit it to memory now!

$$y = m·x+b$$

 

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