A line has slope –. 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 it is A?
a line slope of -5/3...actually I thought it was B...can u explain why it is not...please
Well, let's see if you're right or if you're just "slope-ing" around!
To find out, let's use the slope formula: m = (y2 - y1) / (x2 - x1)
For option A, let's plug in the values:
m = (10 - 13) / (17 - 12)
Simplifying that gives us m = -3 / 5
Oops! That doesn't match the given slope of -1. So, option A is not the right answer.
Let's try option B:
m = (10 - 15) / (13 - 16)
Simplifying that gives us m = 5 / -3
Oh no! That's still not the slope we're looking for. Option B is out too.
Moving on to option C:
m = (10 - 7) / (3 - 0)
Simplifying that gives us m = 3 / 3
Almost there! But 3/3 simplifies to 1, not -1. So option C is not the answer either.
Finally, let's try option D:
m = (18 - 13) / (8 - 11)
Simplifying that gives us m = 5 / -3
Aha! We have a winner! The slope of 5 / -3 matches the slope we're looking for. So, the correct answer is option D, (11, 13) and (8, 18).
Keep practicing, and soon you'll be "sloping" through these questions like a pro!
To determine which two points the line could pass through given a slope of -, we need to find two points that have the same slope when calculated.
The slope of a line can be calculated using the formula:
slope = (change in y-coordinates) / (change in x-coordinates)
Let's calculate the slope for each option:
Option A:
slope = (10 - 13) / (17 - 12) = -3 / 5 = -0.6
Option B:
slope = (10 - 15) / (13 - 16) = -5 / -3 = 1.67
Option C:
slope = (10 - 7) / (3 - 0) = 3 / 3 = 1
Option D:
slope = (18 - 13) / (8 - 11) = 5 / -3 = -1.67
Based on the calculations, we can see that only Option A has a slope of -0.6, which matches the given slope. Therefore, the correct answer is A.
To determine which two points the line with a slope of - passes through, we can use the slope-intercept form of a linear equation: y = mx + b, where m represents the slope.
In this case, your given slope is - (negative one-half). Now we can plug in the coordinates of each point into the equation and check if they satisfy the equation.
Let's check option A:
Point 1: (12, 13) => y = 13, x = 12
13 = -*(12) + b => 13 = -6 + b => b = 19
Therefore, the equation for option A is y = -*(x) + 19
Let's substitute the coordinates of Point 2: (17, 10)
10 = -*(17) + 19 => 10 = -8 + 19 => 10 = 11
The equation doesn't hold true for Point 2, so option A is not correct.
Let's proceed to option B:
Point 1: (16, 15) => y = 15, x = 16
15 = -*(16) + b => 15 = -8 + b => b = 23
Therefore, the equation for option B is y = -*(x) + 23
Substituting the coordinates of Point 2: (13, 10)
10 = -*(13) + 23 => 10 = -6 + 23 => 10 = 17
The equation doesn't hold true for Point 2, so option B is not correct.
Moving on to option C:
Point 1: (0, 7) => y = 7, x = 0
7 = -*(0) + b => 7 = b
Therefore, the equation for option C is y = -(x) + 7
Substituting the coordinates of Point 2: (3, 10)
10 = -*(3) + 7 => 10 = -3 + 7 => 10 = 4
The equation doesn't hold true for Point 2 either, so option C is not correct.
Now let's check option D:
Point 1: (11, 13) => y = 13, x = 11
13 = -*(11) + b => 13 = - + b => b = 24
Therefore, the equation for option D is y = -*(x) + 24
Substituting the coordinates of Point 2: (8, 18)
18 = -*(8) + 24 => 18 = -4 + 24 => 18 = 20
The equation doesn't hold true for Point 2 either, so option D is also not correct.
After analyzing all the options, it is clear that none of the given options satisfy the equation for a line with a slope of -.
Therefore, the answer is none of the above (E).
Note: If the question allows for an approximation, it is possible that one of the options is the best possible answer given the available choices.