The pair of points (6,y) and (10,-1) lies on a line with slope 1/4. What is the value of y?
A. -5
B. -2
C. 2
D. 5
What is the slope of the line that passes through the points (4,2) and (4,-3)
A. -1
B. 0
C. 0
D. Undefined
A line has slope -5/3. Through which two points could this line pass?
A. (12,13) (17,10)
B. (16,15) (13,10)
C. (0,7) (3,10)
D. (11,13) (8,18)
i think is b but i am not sure
To find the value of y in the first question, we can use the slope formula:
slope = (y2 - y1) / (x2 - x1)
In this case, the points are (6, y) and (10, -1), and the slope is 1/4. We can substitute the values into the formula:
1/4 = (-1 - y) / (10 - 6)
To solve for y, we cross-multiply:
4(-1 - y) = 1(10 - 6)
-4 - 4y = 4
-4y = 8
y = -2
Therefore, the value of y is -2. So, the correct answer is B. -2.
For the second question, we need to calculate the slope of the line that passes through the points (4, 2) and (4, -3). In this case, the x-coordinates are the same, which means the line is vertical. A vertical line has an undefined slope, so the correct answer is D. Undefined.
Lastly, to find which two points the line with a slope of -5/3 can pass through, we can use the point-slope form of a line:
(y - y1) = m(x - x1)
where m is the slope. In this case, the slope is -5/3. Let's substitute the values into the equation using each given set of points:
A. (12, 13), (17, 10)
(y - 13) = (-5/3)(x - 12)
We can solve this equation to find the value of y. If y comes out to be 10 when substituting the second point, then this line passes through those two points.
B. (16, 15), (13, 10)
(y - 15) = (-5/3)(x - 16)
C. (0, 7), (3, 10)
(y - 7) = (-5/3)(x - 0)
D. (11, 13), (8, 18)
(y - 13) = (-5/3)(x - 11)
By solving these equations for y, we can determine which pair of points satisfies the equation. The equation that gives y as 10 when substituting (17, 10) is option A. (12, 13) and (17, 10). Therefore, the correct answer is A. (12, 13) (17, 10).
(-1 - y)/(10-6) = 1/4
(-3-2)/(4-4) heavens to mergetroid !
(10-13)/(17-12) = -5/3 ?? I do not think so, try the others