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There are three steps in calculating the slope of a straight line when you are not given its equation. We covered all this in the course of our classes these past few months. Take up the quiz below to polish your skills in solving this math problems and share with your classmates.
Questions and Answers
1.
Find the slope.
Explanation The given answer, 2,2/1, represents the slope of a line. The first number, 2, represents the whole number part of the slope, while the fraction 2/1 represents the fractional part of the slope. This means that the slope is 2 units in the vertical direction and 1 unit in the horizontal direction. Therefore, the line has a steepness of 2 units up for every 1 unit to the right.
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2.
Find the slope.
Explanation The given answer -3,-3/1 represents the slope of a line. In this case, the slope is -3, which means that for every 1 unit increase in the horizontal direction, the line decreases by 3 units in the vertical direction. The fraction -3/1 is another way of representing the same slope, indicating that the line decreases by 3 units vertically for every 1 unit increase horizontally.
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3.
Find the slope.
Explanation The slope is a measure of how steep a line is. In this case, the slope is given as 3/2. This means that for every 3 units the line moves vertically, it also moves 2 units horizontally. Therefore, the line has a positive slope and is relatively steep.
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4.
Find the slope.
Explanation The given answer of -2/5 is the slope of the line. This means that for every unit increase in the horizontal direction, the line decreases by 2/5 units in the vertical direction. The slope is negative, indicating that the line has a downward slope.
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5.
Find the slope.
Explanation The slope is a measure of how steep a line is. In this case, the slope is given as 1/3. This means that for every 1 unit increase in the x-coordinate, the y-coordinate increases by 1/3. It indicates a positive slope, meaning the line is slanting upwards from left to right.
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6.
Find the slope.
Explanation The given answer is the slope of the line. In this case, the slope is -3/1 or -3. The slope represents the steepness of a line, and it is calculated by finding the change in the y-coordinates divided by the change in the x-coordinates. In this case, for every 1 unit increase in the x-coordinate, the y-coordinate decreases by 3 units. Therefore, the slope is -3/1 or -3.
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7.
Find the slope.
Explanation The given answer is the slope of the line. In this case, the slope is 1/5, which means that for every 1 unit increase in the x-coordinate, the y-coordinate increases by 1/5. This indicates a positive slope, meaning the line is rising as it moves from left to right.
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8.
Find the slope.
Explanation The slope is a measure of how steep a line is. In this case, the slope is -1/3, which means that for every 3 units you move horizontally, you move down 1 unit vertically. This indicates a negative slope, which means the line is decreasing as you move from left to right.
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9.
Find the slope.
Explanation The slope of a line represents the rate of change between two points on the line. In this case, the slope is given as 2/5. This means that for every 2 units of change in the vertical direction, there is a corresponding 5 units of change in the horizontal direction. Therefore, the line represented by this slope has a constant slope of 2/5.
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10.
Find the slope.
Explanation The given numbers 9 and 9/1 represent the coordinates of two points on a line. To find the slope of the line, we use the formula (change in y)/(change in x). In this case, the change in y is 9/1 - 9 = 0, and the change in x is 1 - 9 = -8. Therefore, the slope is 0/(-8) = 0.
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11.
Find the slope.Between (-2, -2) and (7, -2).
Explanation The slope between two points is determined by the change in y-coordinates divided by the change in x-coordinates. In this case, both points have the same y-coordinate of -2, indicating a horizontal line. Since the change in y-coordinates is 0, the slope is also 0.
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12.
Find the slope.Between (5, -7) and (6, -4).
Explanation The slope between two points can be found using the formula (y2 - y1) / (x2 - x1). In this case, the coordinates of the first point are (5, -7) and the coordinates of the second point are (6, -4). Plugging these values into the formula, we get (-4 - (-7)) / (6 - 5) = 3 / 1 = 3. Therefore, the slope between these two points is 3.
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13.
Find the slope.Between (20, 3000) and (60, 2000).
Explanation Remember to simplify.
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14.
Find the slope.Between (30, 10) and (50, 20).
Explanation Remember to simplify.
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15.
Find the slope.Between (-2, 3) and (2, -3).
Explanation Remember to simplify
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16.
Find the slope.y = -x - 4
Explanation The given equation is in the form y = mx + b, where m represents the slope. In this case, the slope is -1 because the coefficient of x is -1. Therefore, the slope of the line represented by the equation y = -x - 4 is -1.
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17.
Find the slope.y = 4x + 11
Explanation The slope of a linear equation in the form y = mx + b is represented by the coefficient of x, which in this case is 4. Therefore, the slope of the equation y = 4x + 11 is 4.
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18.
Find the slope.8x + 2y = 96
Explanation The given equation is in the form of a linear equation, which can be written in the form y = mx + b, where m represents the slope of the line. To find the slope, we need to rearrange the equation in this form. By subtracting 8x from both sides and then dividing by 2, we get y = -4x + 48. Therefore, the slope of the line represented by this equation is -4.
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19.
Find the slope.
5x = 90 - 9y
Explanation To find the slope, let's rewrite the equation in slope-intercept form (y = mx + b), where m is the slope:
Given equation: 5x = 90 - 9y
First, let's isolate y:
5x = 90 - 9y
Subtract 90 from both sides:
5x - 90 = -9y
Now, divide both sides by -9:
(5x - 90) / -9 = y
Now, let's rewrite this equation in slope-intercept form:
y = (-5/9)x + 10
Comparing with y = mx + b, we can see that the slope, m, is -5/9. So, the slope of the given equation is -5/9.
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20.
Find the slope.5y = 160 + 9x
Explanation The given equation is in the form of y = mx + b, where m represents the slope. By rearranging the equation, we can isolate the variable y and rewrite it as y = (9/5)x + 32. Therefore, the slope of the equation is 9/5.
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