A line has slope –. Through which two points could this line pass? (1 point) (12, 13), (17, 10) (16, 15), (13, 10) (0, 7), (3, 10) (11, 13), (8, 18)
To determine which two points the line could pass through, we need to find the equation of the line using the given slope.
The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.
Since the slope of the line is -1, we can substitute this into the equation to get y = -x + b.
Now, we can substitute the coordinates of the given points to find the y-intercept b.
Using the first set of points, (12, 13), we have 13 = -12 + b. Solving for b, we find b = 25.
So, the equation of the line is y = -x + 25.
Now we can check which of the remaining points satisfy this equation.
For (17, 10):
y = -x + 25
10 = -17 + 25
10 = 8 (not satisfied)
For (16, 15):
y = -x + 25
15 = -16 + 25
15 = 9 (not satisfied)
For (0, 7):
y = -x + 25
7 = -0 + 25
7 = 25 (not satisfied)
For (11, 13):
y = -x + 25
13 = -11 + 25
13 = 14 (not satisfied)
Therefore, the line could pass through the points (12, 13) and (17, 10).
The pair of points (6, y) and (10, –1) lie on a line with slope . What is the value of y? (1 point) Responses –5 –5 –2 –2 2 2 5
To find the value of y, we can use the formula for finding the slope of a line:
slope = (change in y) / (change in x)
Given that the slope is , we can substitute the values of the coordinates (6, y) and (10, -1) into the formula:
= (y - (-1)) / (6 - 10)
Simplifying this equation gives the following:
= (y + 1) / (-4)
Now we can solve for y by cross-multiplying and simplifying:
(-4) = (y + 1)
-4 = y + 1
y = -5
Therefore, the value of y is -5.
The table below gives the cost per person to rent a fishing charter boat. Find the rate of change given that it is constant. Also, explain what the rate of change means for this situation. People Cost ($) 2 110 3 165 4 220 5 275 (1 point) Responses Image with alt text: The fraction one fifty fifth. Image with alt text: The fraction one hundred ten over one. Image with alt text: The fraction one over two hundred seventy five
To find the rate of change in this situation, we can determine the change in cost divided by the change in the number of people.
Change in cost = $275 - $110 = $165
Change in number of people = 5 - 2 = 3
Rate of change = Change in cost / Change in number of people = $165 / 3 ≈ $55
Therefore, the rate of change in this situation is approximately $55.
The rate of change represents the constant increase in cost per person as the number of people increases. In other words, for every additional person that joins the fishing charter boat, the cost per person increases by approximately $55. This rate of change allows us to determine the cost for any given number of people, assuming the trend remains constant.