How to find a line on a coordinate plane - SSAT Middle Level Quantitative

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Question

Give the slope of the line that passes through and .

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Answer

Use the slope formula, substituting :

$m =\frac{ $y_{2}$$- $y_{1}$ $}{x_{2}$ - $x_{1}$}=\frac{ -3-2 }{-8-4}$ = $\frac{ -5 }{-12}$ = $\frac{5 }{12}$$

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Question

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?

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Answer

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:

and

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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Question

Give the slope of a line that passes through and .

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Answer

Using the slope formula, substituting , , , and :

$m=\frac{4-5}{2-5}$$

Subtract to get:

$m=\frac{-1}{-3}$$

Cancel out the negative signs to get:

$m=\frac{1}{3}$$

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Question

Give the slope of a line that passes through and .

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Answer

Using the slope formula with , , , :

$m=\frac{5-4}{2-(-7)}$$

Subtract to get:

$m=\frac{1}{9}$$

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Question

Give the slope of the line that passes through and .

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Answer

Using the slope formula for

, , , and :

$m=\frac{9-3}{1-(-5)}$$

Combine the negative signs to get:

$m=\frac{9-3}{1+5}$$

Subtract and add to get:

$m=\frac{6}{6}$$

Reduce to get:

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Question

Give the slope of a line that passes through and .

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Answer

Using the slope formula, where is the slope, , and :

$m=\frac{3-7}{2-4}$$

$m=\frac{-4}{-2}$$

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Question

Find the slope of a line with points and .

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Answer

Using the slope formula, where is the slope, , and :

$m=\frac{5-0}{-10-(-1)}$$

$m=\frac{5}{-10+1}$$

$m=-$\frac{5}{9}$$

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Question

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

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Answer

Using the slope formula, where is the slope, , and :

$m=\frac{-4-(-4)}{-5-5}$$

$m=\frac{-4+4}{-10}$$

$m=\frac{0}{-10}$$

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Question

Give the slope of the line that passes through and .

Tap to reveal answer

Answer

Use the slope formula, substituting :

$m =\frac{ $y_{2}$$- $y_{1}$ $}{x_{2}$ - $x_{1}$}=\frac{ -3-2 }{-8-4}$ = $\frac{ -5 }{-12}$ = $\frac{5 }{12}$$

← Didn't Know|Knew It →

Question

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?

Tap to reveal answer

Answer

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:

and

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}$

← Didn't Know|Knew It →

Question

Give the slope of a line that passes through and .

Tap to reveal answer

Answer

Using the slope formula, substituting , , , and :

$m=\frac{4-5}{2-5}$$

Subtract to get:

$m=\frac{-1}{-3}$$

Cancel out the negative signs to get:

$m=\frac{1}{3}$$

← Didn't Know|Knew It →

Question

Give the slope of a line that passes through and .

Tap to reveal answer

Answer

Using the slope formula with , , , :

$m=\frac{5-4}{2-(-7)}$$

Subtract to get:

$m=\frac{1}{9}$$

← Didn't Know|Knew It →

Question

Give the slope of the line that passes through and .

Tap to reveal answer

Answer

Using the slope formula for

, , , and :

$m=\frac{9-3}{1-(-5)}$$

Combine the negative signs to get:

$m=\frac{9-3}{1+5}$$

Subtract and add to get:

$m=\frac{6}{6}$$

Reduce to get:

← Didn't Know|Knew It →

Question

Give the slope of a line that passes through and .

Tap to reveal answer

Answer

Using the slope formula, where is the slope, , and :

$m=\frac{3-7}{2-4}$$

$m=\frac{-4}{-2}$$

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Question

Find the slope of a line with points and .

Tap to reveal answer

Answer

Using the slope formula, where is the slope, , and :

$m=\frac{5-0}{-10-(-1)}$$

$m=\frac{5}{-10+1}$$

$m=-$\frac{5}{9}$$

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Question

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

Tap to reveal answer

Answer

Using the slope formula, where is the slope, , and :

$m=\frac{-4-(-4)}{-5-5}$$

$m=\frac{-4+4}{-10}$$

$m=\frac{0}{-10}$$

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Question

Give the slope of the line that passes through and .

Tap to reveal answer

Answer

Use the slope formula, substituting :

$m =\frac{ $y_{2}$$- $y_{1}$ $}{x_{2}$ - $x_{1}$}=\frac{ -3-2 }{-8-4}$ = $\frac{ -5 }{-12}$ = $\frac{5 }{12}$$

← Didn't Know|Knew It →

Question

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?

Tap to reveal answer

Answer

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:

and

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}$

← Didn't Know|Knew It →

Question

Give the slope of a line that passes through and .

Tap to reveal answer

Answer

Using the slope formula, substituting , , , and :

$m=\frac{4-5}{2-5}$$

Subtract to get:

$m=\frac{-1}{-3}$$

Cancel out the negative signs to get:

$m=\frac{1}{3}$$

← Didn't Know|Knew It →

Question

Give the slope of a line that passes through and .

Tap to reveal answer

Answer

Using the slope formula with , , , :

$m=\frac{5-4}{2-(-7)}$$

Subtract to get:

$m=\frac{1}{9}$$

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