### All SSAT Upper Level Math Resources

## Example Questions

### Example Question #81 : Lines

Find the slope of a line that is perpendicular to the line with the equation .

**Possible Answers:**

**Correct answer:**

Perpendicular lines have slopes that are negative reciprocals of each other. In other words, change the sign and flip the fraction around to find the slope of the line perpendicular to the given one.

### Example Question #82 : Lines

Find the slope of a line that is perpendicular to the line with the equation .

**Possible Answers:**

**Correct answer:**

Perpendicular lines have slopes that are negative reciprocals of each other. In other words, change the sign and flip the fraction around to find the slope of the line perpendicular to the given one.

### Example Question #83 : Lines

Find the slope of a line that is perpendicular to the line with the equation .

**Possible Answers:**

**Correct answer:**

Perpendicular lines have slopes that are negative reciprocals of each other. In other words, change the sign and flip the fraction around to find the slope of the line perpendicular to the given one.

### Example Question #1 : How To Find The Equation Of A Perpendicular Line

What line is perpendicular to *x* + 3*y* = 6 and travels through point (1,5)?

**Possible Answers:**

*y* = 2*x* + 1

*y* = 2/3*x* + 6

*y* = 3*x* + 2

*y* = 6*x* – 3

*y* = –1/3*x* – 4

**Correct answer:**

*y* = 3*x* + 2

Convert the equation to slope intercept form to get *y* = –1/3*x* + 2. The old slope is –1/3 and the new slope is 3. Perpendicular slopes must be opposite reciprocals of each other: *m*_{1 * }*m*_{2} = –1

With the new slope, use the slope intercept form and the point to calculate the intercept: *y* = *mx* + *b* or 5 = 3(1) + *b*, so *b* = 2

So *y* = 3*x* + 2

### Example Question #1 : How To Find The Equation Of A Perpendicular Line

What line is perpendicular to and passes through ?

**Possible Answers:**

**Correct answer:**

Convert the given equation to slope-intercept form.

The slope of this line is . The slope of the line perpendicular to this one will have a slope equal to the negative reciprocal.

The perpendicular slope is .

Plug the new slope and the given point into the slope-intercept form to find the y-intercept.

So the equation of the perpendicular line is .

### Example Question #1 : How To Find The Equation Of A Perpendicular Line

What is the equation of a line that runs perpendicular to the line 2*x* + *y *= 5 and passes through the point (2,7)?

**Possible Answers:**

2*x* – *y* = 6

–*x*/2 + *y* = 6

2*x* + *y* = 7

*x*/2 + *y* = 5

*x*/2 – *y* = 6

**Correct answer:**

–*x*/2 + *y* = 6

First, put the equation of the line given into slope-intercept form by solving for *y*. You get *y* = -2*x* +5, so the slope is –2. Perpendicular lines have opposite-reciprocal slopes, so the slope of the line we want to find is 1/2. Plugging in the point given into the equation *y* = 1/2*x* + *b* and solving for *b*, we get *b* = 6. Thus, the equation of the line is *y* = ½*x* + 6. Rearranged, it is –*x*/2 + *y* = 6.

### Example Question #1 : How To Find The Equation Of A Perpendicular Line

Line *m *passes through the points (1, 4) and (5, 2). If line *p *is perpendicular to *m, *then which of the following could represent the equation for *p?*

**Possible Answers:**

4x **–** 3y = 4

3x + 2y = 4

2x + y = 3

2x **–** y = 3

x **–** y = 3

**Correct answer:**

2x **–** y = 3

The slope of *m* is equal to ^{ } ^{y2-y1}/_{x2-x1}^{ }=^{ 2-4}/_{5-1}^{ }= ^{-1}/_{2}

Since line *p* is perpendicular to line *m*, this means that the products of the slopes of *p* and *m* must be **–**1:

(slope of *p*) * (^{-1}/_{2}) = -1

Slope of *p* = 2

So we must choose the equation that has a slope of 2. If we rewrite the equations in point-slope form (y = mx + b), we see that the equation 2x **–** y = 3 could be written as y = 2x – 3. This means that the slope of the line 2x **– **y =3 would be 2, so it could be the equation of line *p*. The answer is 2x – y = 3.

### Example Question #1 : How To Find The Equation Of A Perpendicular Line

What is the equation for the line that is perpendicular to through point ?

**Possible Answers:**

**Correct answer:**

Perpendicular slopes are opposite reciprocals.

The given slope is found by converting the equation to the slope-intercept form.

The slope of the given line is and the perpendicular slope is .

We can use the given point and the new slope to find the perpendicular equation. Plug in the slope and the given coordinates to solve for the y-intercept.

Using this y-intercept in slope-intercept form, we get out final equation: .

### Example Question #1 : How To Find The Equation Of A Perpendicular Line

Which line below is perpendicular to ?

**Possible Answers:**

**Correct answer:**

The definition of a perpendicular line is one that has a negative, reciprocal slope to another.

For this particular problem, we must first manipulate our initial equation into a more easily recognizable and useful form: slope-intercept form or .

According to our formula, our slope for the original line is . We are looking for an answer that has a perpendicular slope, or an opposite reciprocal. The opposite reciprocal of is . Flip the original and multiply it by .

Our answer will have a slope of . Search the answer choices for in the position of the equation.

is our answer.

(As an aside, the negative reciprocal of 4 is . Place the whole number over one and then flip/negate. This does not apply to the above problem, but should be understood to tackle certain permutations of this problem type where the original slope is an integer.)

### Example Question #7 : How To Find The Equation Of A Perpendicular Line

If a line has an equation of , what is the slope of a line that is perpendicular to the line?

**Possible Answers:**

**Correct answer:**

Putting the first equation in slope-intercept form yields .

A perpendicular line has a slope that is the negative inverse. In this case, .

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