Math / Algebra

QuestionFind the slope of the line passing through the pair of points or state that the slope is undefined. Then indicate whether the line through the points rises, falls, is horizontal, or is vertical. $(-1,1) \text { and }(5,6)$
Select the correct choice below and, if necessary, fill in the answer box within your choice. A. The slope is $\square$ (Simplify your answer.) B. The slope is undefined.
Indicate whether the line through the points rises, falls, is horizontal, or is vertical. A. The line is vertical. B. The line falls from left to right. C. The line is horizontal. D. The line rises from left to right.

Studdy Solution

STEP 1

1. We are given two points: $(-1, 1)$ and $(5, 6)$ .
2. We need to find the slope of the line passing through these points.
3. We need to determine the nature of the line: whether it rises, falls, is horizontal, or is vertical.

STEP 2

1. Recall the formula for the slope between two points.
2. Substitute the given points into the slope formula.
3. Simplify the expression to find the slope.
4. Determine the nature of the line based on the slope.

STEP 3

Recall the formula for the slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ :
$m = \frac{y_2 - y_1}{x_2 - x_1}$

STEP 4

Substitute the given points $(-1, 1)$ and $(5, 6)$ into the slope formula:
Let $(x_1, y_1) = (-1, 1)$ and $(x_2, y_2) = (5, 6)$ .
$m = \frac{6 - 1}{5 - (-1)}$

STEP 5

Simplify the expression to find the slope:
$m = \frac{6 - 1}{5 + 1}$ $m = \frac{5}{6}$
The slope is $\frac{5}{6}$ .

STEP 6

Determine the nature of the line based on the slope:
Since the slope $\frac{5}{6}$ is positive, the line rises from left to right.
Solution: A. The slope is $\frac{5}{6}$ . D. The line rises from left to right.

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Studdy Solution

STEP 1

1. We are given two points: $(-1, 1)$ and $(5, 6)$ .
2. We need to find the slope of the line passing through these points.
3. We need to determine the nature of the line: whether it rises, falls, is horizontal, or is vertical.

STEP 2

1. Recall the formula for the slope between two points.
2. Substitute the given points into the slope formula.
3. Simplify the expression to find the slope.
4. Determine the nature of the line based on the slope.

STEP 3

Recall the formula for the slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ :
$m = \frac{y_2 - y_1}{x_2 - x_1}$

STEP 4

Substitute the given points $(-1, 1)$ and $(5, 6)$ into the slope formula:
Let $(x_1, y_1) = (-1, 1)$ and $(x_2, y_2) = (5, 6)$ .
$m = \frac{6 - 1}{5 - (-1)}$

STEP 5

Simplify the expression to find the slope:
$m = \frac{6 - 1}{5 + 1}$ $m = \frac{5}{6}$
The slope is $\frac{5}{6}$ .

STEP 6

Determine the nature of the line based on the slope:
Since the slope $\frac{5}{6}$ is positive, the line rises from left to right.
Solution: A. The slope is $\frac{5}{6}$ . D. The line rises from left to right.

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Studdy Solution

STEP 1

1. We are given two points: (−1,1)(-1, 1)(−1,1) and (5,6) (5, 6) (5,6).2. We need to find the slope of the line passing through these points.3. We need to determine the nature of the line: whether it rises, falls, is horizontal, or is vertical.

STEP 2

1. Recall the formula for the slope between two points.2. Substitute the given points into the slope formula.3. Simplify the expression to find the slope.4. Determine the nature of the line based on the slope.

STEP 3

Recall the formula for the slope m m m between two points (x1,y1)(x_1, y_1)(x1​,y1​) and (x2,y2)(x_2, y_2)(x2​,y2​):m=y2−y1x2−x1 m = \frac{y_2 - y_1}{x_2 - x_1} m=x2​−x1​y2​−y1​​

STEP 4

Substitute the given points (−1,1)(-1, 1)(−1,1) and (5,6) (5, 6) (5,6) into the slope formula:Let (x1,y1)=(−1,1)(x_1, y_1) = (-1, 1)(x1​,y1​)=(−1,1) and (x2,y2)=(5,6)(x_2, y_2) = (5, 6)(x2​,y2​)=(5,6).m=6−15−(−1) m = \frac{6 - 1}{5 - (-1)} m=5−(−1)6−1​

STEP 5

Simplify the expression to find the slope:m=6−15+1 m = \frac{6 - 1}{5 + 1} m=5+16−1​ m=56 m = \frac{5}{6} m=65​The slope is 56\frac{5}{6}65​.

STEP 6

Determine the nature of the line based on the slope:Since the slope 56\frac{5}{6}65​ is positive, the line rises from left to right. Solution: A. The slope is 56\frac{5}{6}65​. D. The line rises from left to right.

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1. We are given two points: $(-1, 1)$ and $(5, 6)$ .
2. We need to find the slope of the line passing through these points.
3. We need to determine the nature of the line: whether it rises, falls, is horizontal, or is vertical.

1. Recall the formula for the slope between two points.
2. Substitute the given points into the slope formula.
3. Simplify the expression to find the slope.
4. Determine the nature of the line based on the slope.

Recall the formula for the slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ :
$m = \frac{y_2 - y_1}{x_2 - x_1}$

Substitute the given points $(-1, 1)$ and $(5, 6)$ into the slope formula:
Let $(x_1, y_1) = (-1, 1)$ and $(x_2, y_2) = (5, 6)$ .
$m = \frac{6 - 1}{5 - (-1)}$

Simplify the expression to find the slope:
$m = \frac{6 - 1}{5 + 1}$ $m = \frac{5}{6}$
The slope is $\frac{5}{6}$ .

Determine the nature of the line based on the slope:
Since the slope $\frac{5}{6}$ is positive, the line rises from left to right.
Solution: A. The slope is $\frac{5}{6}$ . D. The line rises from left to right.