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

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

Vt_custom_xy_xylinesegment1

Which equation of a line is parallel to line segment $\bar{AB}$ ?

Possible Answers:

$y=\frac{9}{13}-8$

$y=\frac{13}{9}+5$

$y=-\frac{9}{13}-6$

$y=\frac{5}{12}+4$

Correct answer:

$y=\frac{9}{13}-8$

解释:

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 $\bar{AB}$ .

Since, line segment $\bar{AB}$ has a slope of $\frac{9}{13}$ the correct equation is: $y=\frac{9}{13}-8$

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

Vt_custom_xy_xysegment_3

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

Possible Answers:

x=-7

y=-7

y=7

x=7

Correct answer:

y=-7

解释:

The above line segment is a horizontal line that passes through theaxis at -7. Since this line is horizontal, it does not have a slope. Therefore, y=-7 is the correct answer.

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

Vt_custom_xy_xysegment_3

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

Possible Answers:

y=7

y=-7

$y=-\frac{1}{2}-7$

x=-3

Correct answer:

x=-3

解释:

自线segment is horizontal, the equation that is perpendicular to the segment must run vertically. The only linear equation that runs vertically (perpendicular to y=-7 ) is x=-3 .

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

Vt_custom_xy_xysegment_3

At what coordinate point does the line x=-3 intersect with the line segment shown above?

Possible Answers:

(-3,-7)

(-7,-3)

(3,7)

(3,-7)

Correct answer:

(-3,-7)

解释:

Since, x=-3 is perpendicular to y=-7 the points must cross at (-3,-7) , because it is the only coordinate point that both lines pass through.

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Example Question #141 :Coordinate Geometry

Vt_custom_xy_xyline5

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

Possible Answers:

(3,0)

(0,-2)

(-3,0)

(0,3)

Correct answer:

(3,0)

解释:

Keep in mind that the values in the coordinate points are (x,y) thus the point (3,0) is the point at which the line segment passes through theaxis.

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

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

Possible Answers:

$y=\frac{3}{4}x-7$

$y=\frac{3}{4}x+5$

$y=\frac{3}{4}x-5$

$y=\frac{3}{4}x+7$

Correct answer:

$y=\frac{3}{4}x-7$

解释:

To identify the correct equation, apply the formula y=mx+b , whererepresents the slope of the line andtheintercept.

Thus, the line that passes through theaxis at (0,-7) is $y=\frac{3}{4}x-7$

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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:

$y=\frac{8}{4}x+4$

$y=-\frac{3}{8}x+4$

$y=-\frac{3}{4}x+8$

$y=-\frac{8}{3}x+4$

Correct answer:

$y=-\frac{8}{3}x+4$

解释:

To find which equation of a line has the steepest slope, apply the formula: y=mx+b , whererepresents the slope of the line andrepresents theintercept.

Also, note that $m=\frac{rise}{run}$ , meaning the change in thevalue, over the change in thevalue.

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

Thus, the equation $y=-\frac{8}{3}x+4$ has the steepest slope, because in order to go from one point to the next move a vertical distance ofand a horizontal distance ofwhich is larger than any of the other choices.

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

Find the slope of the line that passes through the coordinate points (-3,4) and (2,-1) .

Possible Answers:

$-\frac{1}{2}$

$\frac{1}{2}$

Correct answer:

解释:

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

$Slope=\frac{y_2-y_1}{x_2-x_1}$

Thus the correct answer is:

$\frac{ -1-4}{2--3}=\frac{-5}{5}=-\frac{5}{5}=-1$

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

Vt_custom_xy_xylinesegment1

Line segment $\bar{AB}$ has endpoints (-6,-3) and (7,6) . What is the slope of the line segment?

Possible Answers:

$-\frac{9}{13}$

$\frac{9}{13}$

$\frac{1}{3}$

$\frac{13}{9}$

Correct answer:

$\frac{9}{13}$

解释:

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

$Slope=\frac{y_2-y_1}{x_2-x_1}$

Thus the correct answer is:
$\frac{6--3}{7--6}=\frac{6+3}{7+6}=\frac{9}{13}$

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

Vt_custom_xy_xysegment_3

Find the length of the line segment above.

Possible Answers:

Correct answer:

解释:

To find the length of this line segment find the difference between each of the two end pointsvalues, since they have the samevalue.

The difference betweenandis.

9-(-8)=9+8=17

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

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

All ISEE Lower Level Quantitative Resources

Example Questions

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

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

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

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

Example Question #141 :Coordinate Geometry

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

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

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

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

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

All ISEE Lower Level Quantitative Resources

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