ISEE Middle Level Quantitative : How to find a line on a coordinate plane

Study concepts, example questions & explanations for ISEE Middle Level Quantitative

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Example Questions

Example Question #1 : How To Find A Line On A Coordinate Plane

Give the equation of the line through point  that has slope .

Possible Answers:

Correct answer:

Explanation:

Use the point-slope formula with 

Example Question #2 : How To Find A Line On A Coordinate Plane

Which is the greater quantity?

(A) The slope of the line 

(B) The slope of the line 

Possible Answers:

(A) and (B) are equal

It is impossible to determine which is greater from the information given

(B) is greater

(A) is greater

Correct answer:

(A) is greater

Explanation:

Rewrite each in the slope-intercept form,  will be the slope.

The slope of this line is .

 

The slope of this line is .

 

Since , (A) is greater.

Example Question #3 : How To Find A Line On A Coordinate Plane

Which is the greater quantity?

(A) The slope of the line 

(B) The slope of the line 

Possible Answers:

(A) and (B) are equal

(A) is greater

It is impossible to determine which is greater from the information given

(B) is greater

Correct answer:

(A) and (B) are equal

Explanation:

Rewrite each in the slope-intercept form,  will be the slope.

The slope of the line of  is 

 

The slope of the line of  is also 

 

The slopes are equal.

Example Question #4 : How To Find A Line On A Coordinate Plane

 and  are positive integers, and . Which is the greater quantity?

(a) The slope of the line on the coordinate plane through the points  and .

(b) The slope of the line on the coordinate plane through the points  and .

Possible Answers:

It is impossible to determine which is greater from the information given

(a) is the greater quantity

(b) is the greater quantity

(a) and (b) are equal

Correct answer:

(a) and (b) are equal

Explanation:

The slope of a line through the points  and  can be found by setting 

in the slope formula:

The slope of a line through the points  and  can be found similarly:

The lines have the same slope.

Example Question #5 : How To Find A Line On A Coordinate Plane

A line passes through the points with coordinates  and , where . Which expression is equal to the slope of the line?

Possible Answers:

Undefined

Correct answer:

Explanation:

The slope of a line through the points  and , can be found by setting 

:

in the slope formula:

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