The pair of points (6, y) and (10, –1) lie on a line with slope 1/4 the value of y?
(1 point)
–5
–2
2
5
To find the slope of the line passing through the points (6, y) and (10, -1), we can use the formula for slope:
slope = (change in y)/(change in x)
By substituting the x and y coordinates of the two points, we get:
slope = (y - (-1))/(6 - 10) = (y + 1)/(-4)
We are given that this slope is equal to 1/4 the value of y. So we can set up the following equation:
(y + 1)/(-4) = 1/4 * y
By cross-multiplying, we get:
4(y + 1) = -4y
Expanding and simplifying, we get:
4y + 4 = -4y
Combining like terms, we get:
8y = -4
Dividing both sides by 8, we get:
y = -4/8 = -1/2
Thus, the value of y is -1/2.
Therefore, the pair of points (6, y) and (10, –1) lie on a line with slope 1/4 the value of y when y = -1/2.
Plug in the value of y = -1/2 into the slope equation to confirm:
slope = (y + 1)/(-4) = (-1/2 + 1)/(-4) = 1/2 * 1/(-4) = 1/8
The slope of the line is 1/8, which is equal to 1/4 the value of -1/2. So the answer is -2.
What is the slope of a vertical line?
(1 point)
–1
0
1
undefined
The slope of a vertical line is undefined.
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.
2 l 110
3 l165
4 l 220
5 l 275
A. 1/55
B.110/1
C.1/275
D.55/1
To find the rate of change in this situation, we can calculate the difference in cost per person between any two points and then calculate the ratio of that difference to the corresponding change in the number of people.
Looking at the table, we see that the cost per person increases by $55 as the number of people increases by 1. Therefore, the rate of change is $55 per person.
So, the correct answer is A. 1/55.
The rate of change in this situation means that for each additional person on the fishing charter boat, the cost per person increases by $55.