The SAT will test your ability to manipulate linear equations. You may be required to change the slope, y-intercept, or reflect a line across an axis. Remember that parallel lines have the same slope, and perpendicular lines have slopes that are the negative reciprocals of each other.

For example:

Which could be the equation of a line with 3 times the slope of the line represented by \(2x-3y=7\)?

A) \(y=6x+21\)

B) \(y=\frac23x-7\)

C) \(y=2x–10\)

D) \(y=-6x–21\)

**Strategy:**

**You will almost always need to put the original equation, and the answer choices, in slope-intercept form (**\(y=mx+b\)**).**

To solve our example above, we subtract 2*x* from both sides and then divide by -3.

$$y=\frac23x-\frac73$$

Remember the question asked us for 3 times the slope, so we multiply (\\frac23\times3=2\). The only possible equation is C).

Use the same approach for **perpendicular** lines.

$$-4x+6y=8$$

In the *xy*-plane, the graph of which of the following equations is perpendicular to the graph of the equation above.

A) \(3x+2y=6\)

B) \(2x–3y=9\)

C) \(2x+3y=4\)

D) \(4x+4y=8\)

First, we have to put the equation in the question into slope-intercept form by adding 4*x* to both sides and then dividing by 6. This gives us a slope of \(\frac23\). Since we know the equation of a perpendicular slope is the negative reciprocal (in this case, \(\frac{-2}3\)), we must put each answer into slope-intercept form until we find the right one. Unfortunately, there isn’t a shortcut on these problems – you just have to work through each answer until you have the right slope.** A**) is our correct answer in this case.

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