SAT Math – Algebra: Linear Equations in Two Variables | SAT Practice | Medium-Difficulty Questions with Answers

Question ID 002dba45
Assessment Test Domain Skill Difficulty

SAT Math Algebra Linear equations in
two variables


ID: 002dba45

Line is defined by . Line is perpendicular to line in the xy-plane. What is the slope of line ?


ID: 002dba45 Answer
Correct Answer: .1764, .1765, 3/17

Rationale

The correct answer is . It’s given that line is perpendicular to line in the xy-plane. This means that the
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slope of line is the negative reciprocal of the slope of line . The equation of line , , is written in
slope-intercept form , where is the slope of the line and is the y-coordinate of the y-intercept of
the line. It follows that the slope of line is . The negative reciprocal of a number is divided by the
number. Therefore, the negative reciprocal of is , or . Thus, the slope of line is . Note that 3/17,
.1764, .1765, and 0.176 are examples of ways to enter a correct answer.
O

Question Difficulty: Medium
FD
O
C

,Question ID 01682aa5
Assessment Test Domain Skill Difficulty

SAT Math Algebra Linear equations in
two variables


ID: 01682aa5

Line is defined by . Line is perpendicular to line in the xy-plane. What is the slope of line ?

A.

B.

C.

D.
PR

ID: 01682aa5 Answer
Correct Answer: C

Rationale
O

Choice C is correct. It’s given that line is perpendicular to line in the xy-plane. This means that the slope of
line is the negative reciprocal of the slope of line . If the equation for line is rewritten in slope-intercept
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form , where and are constants, then is the slope of the line and is its y-intercept.
Subtracting from both sides of the equation yields . Dividing both sides of this
equation by yields . It follows that the slope of line is . The negative reciprocal of a number is
divided by the number. Therefore, the negative reciprocal of is , or . Thus, the slope of line is .
O

Choice A is incorrect. This is the slope of line , not line .

Choice B is incorrect. This is the reciprocal, not the negative reciprocal, of the slope of line .
C

Choice D is incorrect. This is the negative, not the negative reciprocal, of the slope of line .

Question Difficulty: Medium

, Question ID 9f3cb472
Assessment Test Domain Skill Difficulty

SAT Math Algebra Linear equations in
two variables


ID: 9f3cb472

Line in the xy-plane has a slope of and passes through the point . Which equation defines line ?

A.

B.

C.

D.
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ID: 9f3cb472 Answer
Correct Answer: D

Rationale
O

Choice D is correct. The equation that defines line in the xy-plane can be written in slope-intercept form
, where is the slope of line and is its y-intercept. It’s given that line has a slope of .
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Therefore, . Substituting for in the equation yields , or . It’s
also given that line passes through the point . Substituting for and for in the equation
yields , or . Adding to both sides of this equation yields .
Substituting for in the equation yields .
O

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect. This equation defines a line that has a slope of , not , and passes through the point
C

, not .

Choice C is incorrect. This equation defines a line that passes through the point , not .

Question Difficulty: Medium