How to find a line on a coordinate plane

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

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Give the slope of a line that passes through and .

$\frac{1}{3}$

CORRECT

$\frac{1}{2}$

$\frac{3}{4}$

$\frac{2}{5}$

$\frac{4}{5}$

Explanation

Using the slope formula, substituting $x_{1}=5$ , $x_{2}=2$ , $y_{1}=5$ , and $y_{2}=4$ :

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

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

Subtract to get:

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

Cancel out the negative signs to get:

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

Give the slope of a line that passes through and .

CORRECT

$\frac{1}{2}$

$-\frac{1}{2}$

$\frac{3}{7}$

Explanation

Using the slope formula, where is the slope, $(x_{1},y_{1})=$ , and $(x_{2},y_{2})=$ :

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

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

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

Give the slope of a line that passes through and .

$\frac{1}{9}$

CORRECT

$\frac{2}{9}$

$\frac{4}{7}$

$\frac{3}{8}$

$\frac{5}{7}$

Explanation

Using the slope formula with $x_{1}=-7$ , $x_{2}=2$ , $y_{1}=4$ , $y_{2}=5$ :

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

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

Subtract to get:

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

Give the slope of the line that passes through and .

CORRECT

$\frac{1}{2}$

$\frac{3}{2}$

$-\frac{1}{2}$

$-\frac{3}{4}$

Explanation

Using the slope formula for

$x_{1}=-5$ , $x_{2}=1$ , $y_{1}=3$ , and $y_{2}=9$ :

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

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

Combine the negative signs to get:

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

Subtract and add to get:

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

Reduce to get:

Find the slope of a line with points and .

$-\frac{5}{9}$

CORRECT

$\frac{5}9 {}$

$\frac{9}{5}$

$-\frac{9}{5}$

Cannot be determined

Explanation

Using the slope formula, where is the slope, $(x_{1},y_{1})=$ , and $(x_{2},y_{2})=$ :

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

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

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

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

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?

$\frac{1}{3}$

CORRECT

$\frac{3}{18}$

$\frac{1}{18}$

$\frac{5}{9}$

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 $(x_{2}, y_{2})= (18,9)$