1. Is it more difficult to run up a ramp with a slope of 1/5 or a slope of 5?
2. What is the slope of a line that passes through the points (2,0) and (5,0)?
3. A line has a slope of 2. It passes through the points (1,2) and (3,y). What is he value of y?
4. What is the slope of a line that passes through the points (2,0) and (5,0)?
slope of 5 is much steeper, right?
y=mx+b
y=2x+b
for 1,2
2=2*1)+b or b=zero
for 3,y
y=2*3=6 your teacher is too easy.
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Is it more diffcault to run up a ramp of 1/5 or 5
1. To determine which ramp is more difficult to run up, we need to compare the slopes. The slope of a ramp determines the steepness of the incline.
To calculate the slope, we use the formula: slope = change in vertical distance / change in horizontal distance.
For a ramp with a slope of 1/5, this means for every 1 unit increase in vertical distance, there is a 5 unit increase in horizontal distance.
On the other hand, for a ramp with a slope of 5, there is a 5 unit increase in vertical distance for every 1 unit increase in horizontal distance.
Comparing the two, it is more difficult to run up the ramp with a slope of 5 because it is steeper and involves a greater increase in vertical distance for each unit of horizontal distance.
2. To find the slope of a line passing through two points (x1, y1) and (x2, y2), we use the formula: slope = (y2 - y1) / (x2 - x1).
In this case, we have the points (2, 0) and (5, 0). Plugging their coordinates into the formula, we get:
slope = (0 - 0) / (5 - 2) = 0 / 3 = 0.
Therefore, the slope of the line passing through the points (2, 0) and (5, 0) is 0.
3. Let's use the slope-intercept form of a line, y = mx + b, where m represents the slope and b represents the y-intercept.
We are given that the line passes through the points (1, 2) and (3, y), and its slope is 2. Using the formula, we have:
2 = (y - 2) / (3 - 1).
To solve for y, we cross-multiply and simplify the equation:
2(3 - 1) = y - 2,
4 = y - 2,
y = 4 + 2,
y = 6.
Therefore, the value of y is 6.
4. The slope of a line passing through the points (2, 0) and (5, 0) can be calculated using the slope formula: slope = (y2 - y1) / (x2 - x1).
In this case, the y-coordinates of both points are 0, so the numerator becomes 0 - 0 = 0.
The x-coordinates are 2 and 5, respectively, so the denominator becomes 5 - 2 = 3.
So, the slope = 0 / 3 = 0.
Therefore, the slope of the line passing through the points (2, 0) and (5, 0) is 0.