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

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

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Example Questions

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

Give the slope of the line that passes through (5,3) and (-1, 5) .

Possible Answers:

$-\frac{1}{3}$

$\frac{1}{3}$

$\frac{4}{3}$

Correct answer:

$-\frac{1}{3}$

Explanation:

Use the slope formula, substituting $x_{1}= 5, y_{1}=3,x_{2}= -1, y_{2}=5$ :

$m =\frac{ y_{2}- y_{1} }{x_{2} - x_{1}}=\frac{ 5-3 }{-1-5} = \frac{ 2 }{-6} =-\frac{1 }{3}$

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Example Question #1 : Coordinate Geometry

What is the slope of the line that passes through (4,4) and (8,8) ?

Possible Answers:

1.5

0.5

2.5

Correct answer:

Explanation:

We can use the slope formula:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{8-4}{8-4}=\frac{4}{4}=1$

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Example Question #2 : Coordinate Geometry

What is the slope of the line that passes through (4,7) and (-3,-7) ?

Possible Answers:

1.5

3.5

Correct answer:

Explanation:

We can use the slope formula:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{-7-7}{-3-4}=\frac{-14}{-7}=2$

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

Find the slope of the line that passes through coordinates (-4,-3) and (8,-4) .

Possible Answers:

$m= -\frac{1}{12}$

$m= -\frac{1}{2}$

m = 2

m = -2

Correct answer:

$m= -\frac{1}{12}$

Explanation:

The formula for slope is:

$m = \frac{y_{2} - y_{1}}{x_{2}-x_{1}}$

In this particular question our values are given as follows.

$y_{2} = -4$

$y_{1} =-3$

$x_{2} = 8$

$x_{1} = -4$

Substituting the above values into the formula for slope we get,

$\frac{-4 - (-3)}{8- (-4)} = \frac{-1}{12}$

$m = -\frac{1}{12}$ .

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

Billy set up a ramp for his toy cars. He did this by taking a wooden plank and putting one end on top of a brick that was 3 inches high. He then put the other end on top of a box that was 9 inches high. The bricks were 18 inches apart. What is the slope of the plank?

Possible Answers:

$\frac{1}{18}$

$\frac{1}{3}$

$\frac{5}{9}$

$\frac{3}{18}$

Correct answer:

$\frac{1}{3}$

Explanation:

The value of the slope (m) is rise over run, and can be calculated with the formula below:

$m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

The coordinates of the first end of the plank would be (0,3), given that this is the starting point of the plank (so x would be 0), and y would be 3 since the brick is 3 inches tall.

The coordinates of the second end of the plank would be (18,9) since the plank is 18 inches long (so x would be 18) and y would be 9 since the box was 9 inches tall at the other end.

From this information we know that we can assign the following coordinates for the equation:

$\left(x_{1},y_{1}\right) = (0,3)$ and $(x_{2}, y_{2})= (18,9)$

Below is the solution we would get from plugging this information into the equation for slope:

$m = \frac{9-3}{18-0}}$

This reduces to $\frac{6}{18} =\frac{1}{3}$

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Example Question #291 : Geometry

What is the slope of the line depicted by the graph?

Screen shot 2016 02 10 at 9.35.05 am

Possible Answers:

$\frac{8}{5}$

$\frac{5}{8}$

Correct answer:

$\frac{5}{8}$

Explanation:

Looking at the graph, it is seen that the line passes through the points (-8,-5) and (8,5).

Screen shot 2016 02 10 at 9.35.05 am

The slope of a line through the points (8, 5) and (-8,- 5) can be found by setting

$x_{1} = -8,y_{1} = -5, x_{2} = 8, y_{2} = 5$ :

in the slope formula:

$m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}} = \frac{5-(-5)}{8 - (-8)} = \frac{5+5}{8 + 8} = \frac{10}{16} = \frac{5}{8}$

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

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

All ISEE Middle Level Math Resources

Example Questions

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

Example Question #1 : Coordinate Geometry

Example Question #2 : Coordinate Geometry

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

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

Example Question #291 : Geometry

All ISEE Middle Level Math Resources

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