Finding the Slope Given Two Points

1. What is the slope of the line passing through the points (4,2), (8,4)?

The slope of a line passing through two points can be found using the formula (y2 - y1) / (x2 - x1). In this case, the coordinates of the two points are (4,2) and (8,4). Plugging these values into the formula, we get (4 - 2) / (8 - 4) = 2 / 4 = 1/2. Therefore, the slope of the line passing through these points is 1/2.

Explanation

The slope of a line passing through two points can be found using the formula (y2 - y1) / (x2 - x1). In this case, the coordinates of the two points are (4,2) and (8,4). Plugging these values into the formula, we get (4 - 2) / (8 - 4) = 2 / 4 = 1/2. Therefore, the slope of the line passing through these points is 1/2.

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2. The slope of the line passing through the points (1,4), (-7,4) is...

The slope of a line passing through two points can be found using the formula (y2-y1)/(x2-x1). In this case, the y-coordinates of both points are the same, which means that the line is horizontal. When the line is horizontal, the difference in y-coordinates is always 0. Therefore, the slope of the line passing through the given points is 0.

Explanation

The slope of a line passing through two points can be found using the formula (y2-y1)/(x2-x1). In this case, the y-coordinates of both points are the same, which means that the line is horizontal. When the line is horizontal, the difference in y-coordinates is always 0. Therefore, the slope of the line passing through the given points is 0.

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3. Identify the slope of this equation: y = 3/5x - 6

The slope of the equation y = 3/5x - 6 is 3/5. The slope represents the rate at which the y-coordinate changes with respect to the x-coordinate. In this equation, the coefficient of x is 3/5, which means that for every increase of 1 in the x-coordinate, the y-coordinate increases by 3/5. Therefore, the slope of the equation is 3/5.

Explanation

The slope of the equation y = 3/5x - 6 is 3/5. The slope represents the rate at which the y-coordinate changes with respect to the x-coordinate. In this equation, the coefficient of x is 3/5, which means that for every increase of 1 in the x-coordinate, the y-coordinate increases by 3/5. Therefore, the slope of the equation is 3/5.

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4. Find the slope of the line passing through the points (2,1), (0,1).

The points (2,1) and (0,1) have the same y-coordinate, which means they lie on a horizontal line. A horizontal line has a slope of 0, as it does not rise or fall in the y-direction. Therefore, the slope of the line passing through these points is 0.

Explanation

The points (2,1) and (0,1) have the same y-coordinate, which means they lie on a horizontal line. A horizontal line has a slope of 0, as it does not rise or fall in the y-direction. Therefore, the slope of the line passing through these points is 0.

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5. Find the slope of the line passing through the points (-3,-3), (2,2).

The slope of a line passing through two points can be found using the formula: slope = (change in y-coordinates)/(change in x-coordinates). In this case, the change in y-coordinates is 2 - (-3) = 5, and the change in x-coordinates is 2 - (-3) = 5. Therefore, the slope of the line passing through the points (-3,-3) and (2,2) is 5/5 = 1.

Explanation

The slope of a line passing through two points can be found using the formula: slope = (change in y-coordinates)/(change in x-coordinates). In this case, the change in y-coordinates is 2 - (-3) = 5, and the change in x-coordinates is 2 - (-3) = 5. Therefore, the slope of the line passing through the points (-3,-3) and (2,2) is 5/5 = 1.

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6. The slope of the line passing through the points (3,9), (-1,7)

The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) can be calculated using the formula (y₂ - y₁) / (x₂ - x₁). In this case, the points are (3,9) and (-1,7). Plugging the values into the formula, we get (7 - 9) / (-1 - 3) = -2 / -4 = 1/2. Therefore, the slope of the line passing through these points is 1/2.

Explanation

The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) can be calculated using the formula (y₂ - y₁) / (x₂ - x₁). In this case, the points are (3,9) and (-1,7). Plugging the values into the formula, we get (7 - 9) / (-1 - 3) = -2 / -4 = 1/2. Therefore, the slope of the line passing through these points is 1/2.

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7. Identify the y-intercept of the equation: y = 3/5x - 1

The y-intercept of an equation represents the point where the line crosses the y-axis. In the given equation, y = 3/5x - 1, the y-intercept is -1. This means that when x is 0, the value of y is -1.

Explanation

The y-intercept of an equation represents the point where the line crosses the y-axis. In the given equation, y = 3/5x - 1, the y-intercept is -1. This means that when x is 0, the value of y is -1.

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8. Put this equation into y = mx + b form: -2x + y = 5

The given equation, -2x + y = 5, can be rearranged into y = 2x + 5 form by isolating the y variable. By adding 2x to both sides of the equation, we get y = 2x + 5. This equation represents a linear function in slope-intercept form, where the coefficient of x is the slope (2) and the constant term (5) is the y-intercept. Therefore, the correct answer is y = 2x + 5.

Explanation

The given equation, -2x + y = 5, can be rearranged into y = 2x + 5 form by isolating the y variable. By adding 2x to both sides of the equation, we get y = 2x + 5. This equation represents a linear function in slope-intercept form, where the coefficient of x is the slope (2) and the constant term (5) is the y-intercept. Therefore, the correct answer is y = 2x + 5.

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9. Find the slope of the line passing through the points (2,5), (2,8).

The slope of a line is determined by the change in y-coordinates divided by the change in x-coordinates between two points on the line. In this case, the x-coordinates of the two given points are the same (both 2), which means the change in x is 0. When the change in x is 0, the slope is undefined because division by zero is undefined in mathematics. Therefore, the slope of the line passing through the points (2,5) and (2,8) is undefined.

Explanation

The slope of a line is determined by the change in y-coordinates divided by the change in x-coordinates between two points on the line. In this case, the x-coordinates of the two given points are the same (both 2), which means the change in x is 0. When the change in x is 0, the slope is undefined because division by zero is undefined in mathematics. Therefore, the slope of the line passing through the points (2,5) and (2,8) is undefined.

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10. The slope of the line passing through the points (1,9), (-3,5)

The slope of a line passing through two points can be found using the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. In this case, the coordinates are (1,9) and (-3,5). Plugging these values into the formula, we get (5 - 9) / (-3 - 1) = -4 / -4 = 1. Therefore, the slope of the line passing through these points is 1.

Explanation

The slope of a line passing through two points can be found using the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. In this case, the coordinates are (1,9) and (-3,5). Plugging these values into the formula, we get (5 - 9) / (-3 - 1) = -4 / -4 = 1. Therefore, the slope of the line passing through these points is 1.

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11. The slope of the line passing through the points (6,-9), (-3,1)

The slope of a line passing through two points can be found using the formula (y2 - y1) / (x2 - x1). In this case, the coordinates of the two points are (6, -9) and (-3, 1). Plugging these values into the formula, we get (-9 - 1) / (6 - (-3)) = -10/9. Therefore, the slope of the line passing through these points is -10/9.

Explanation

The slope of a line passing through two points can be found using the formula (y2 - y1) / (x2 - x1). In this case, the coordinates of the two points are (6, -9) and (-3, 1). Plugging these values into the formula, we get (-9 - 1) / (6 - (-3)) = -10/9. Therefore, the slope of the line passing through these points is -10/9.

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12. Find the slope of the line passing through the points (5,-1), (-2,-3).

To find the slope of a line passing through two points, we can use the formula: slope = (y2-y1)/(x2-x1). In this case, the coordinates of the two points are (5,-1) and (-2,-3). Plugging these values into the formula, we get: slope = (-3-(-1))/(-2-5) = (-3+1)/(-2-5) = -2/-7 = 2/7. Therefore, the slope of the line passing through these two points is 2/7.

Explanation

To find the slope of a line passing through two points, we can use the formula: slope = (y2-y1)/(x2-x1). In this case, the coordinates of the two points are (5,-1) and (-2,-3). Plugging these values into the formula, we get: slope = (-3-(-1))/(-2-5) = (-3+1)/(-2-5) = -2/-7 = 2/7. Therefore, the slope of the line passing through these two points is 2/7.

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13. Find the slope of the line passing through the points (-6,2), (0,-6).

To find the slope of a line passing through two points, we can use the formula: slope = (y2 - y1) / (x2 - x1). In this case, the coordinates of the two points are (-6,2) and (0,-6). Using the formula, we can substitute the values: slope = (-6 - 2) / (0 - (-6)) = -8 / 6 = -4 / 3. Therefore, the slope of the line passing through these two points is -4/3.

Explanation

To find the slope of a line passing through two points, we can use the formula: slope = (y2 - y1) / (x2 - x1). In this case, the coordinates of the two points are (-6,2) and (0,-6). Using the formula, we can substitute the values: slope = (-6 - 2) / (0 - (-6)) = -8 / 6 = -4 / 3. Therefore, the slope of the line passing through these two points is -4/3.

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Finding The Slope Given Two Points