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

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

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Example Questions

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

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Which equation of a line is parallel to line segment ?  

Possible Answers:

Correct answer:

Explanation:

In order for the equation to represent a line that is parallel to the line that is shown, the equation must have the same slope as line segment 

Since, line segment  has a slope of , the correct equation is: 

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

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The points in the above line segment are apart of which of the following linear equations? 

Possible Answers:

Correct answer:

Explanation:

The above line segment is a horizontal line that passes through the  axis at  Since this line is horizontal, it does not have a slope. Therefore,  is the correct answer. 

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

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Which of the following linear equations is perpendicular to the line segment shown above? 

Possible Answers:

Correct answer:

Explanation:

Since the line segment is horizontal, the equation that is perpendicular to the segment must run vertically. The only linear equation that runs vertically (perpendicular to ) is .

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

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At what coordinate point does the line  intersect with the line segment shown above? 

Possible Answers:

Correct answer:

Explanation:

Since,  is perpendicular to  the points must cross at , because it is the only coordinate point that both lines pass through. 

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

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At which coordinate point does this line segment cross the -axis? 

Possible Answers:

Correct answer:

Explanation:

Keep in mind that the values in the coordinate points are , thus the point  is the point at which the line segment passes through the  axis. 

Example Question #6 : How To Find A Line On A Coordinate Plane

Find the equation that represents a line that has a  intercept of .

Possible Answers:

Correct answer:

Explanation:

To identify the correct equation, apply the formula , where  represents the slope of the line and  the  intercept. 

Thus, the line that passes through the  axis at  is 

Example Question #7 : How To Find A Line On A Coordinate Plane

Which of the following equations of a line has the steepest slope? 

Possible Answers:

Correct answer:

Explanation:

To find which equation of a line has the steepest slope, apply the formula: , where  represents the slope of the line and  represents the  intercept.

Also, note that , meaning the change in the  value, over the change in the  value. 

The equation that has the largest absolute value of m is the equation that has the steepest slope.

Thus, the equation  has the steepest slope, because in order to go from one point to the next move a vertical distance of  and a horizontal distance of  which is larger than any of the other choices. 

Example Question #8 : How To Find A Line On A Coordinate Plane

Find the slope of the line that passes through the coordinate points  and .

Possible Answers:

Correct answer:

Explanation:

To find the slope of the line that passes through these two coordinate points, apply the formula: 



Thus the correct answer is:

Example Question #9 : How To Find A Line On A Coordinate Plane

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Line segment  has endpoints  and . What is the slope of the line segment? 

Possible Answers:

Correct answer:

Explanation:

To find the slope of the line that passes through these two coordinate points, apply the formula: 



Thus the correct answer is:

Example Question #10 : How To Find A Line On A Coordinate Plane

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Find the length of the line segment above. 

 

Possible Answers:

Correct answer:

Explanation:

To find the length of this line segment find the difference between each of the two end points  values, since they have the same  value. 

The difference between  and  is .

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