A line has slope . Through which two points could this line pass? (1 point) Responses (12, 13) and (17, 10) (12, 13) and (17, 10) (16, 15) and (13, 10) (16, 15) and (13, 10) (0, 7) and (3, 10) (0, 7) and (3, 10) (11, 13) and (8, 18)
The two points through which a line with a given slope could pass can be determined by using the slope-intercept form of a linear equation: y = mx + b, where m represents the slope of the line.
In this case, the given slope is not provided, so it is not possible to determine the specific two points through which the line could pass.
A line has slope . Through which two points could this line pass? (1 point)
Responses
(12, 13) and (17, 10)
(16, 15) and (13, 10)
(0, 7) and (3, 10)
(11, 13) and (8, 18)
Apologies for the incorrect initial response. It seems the value for the slope is missing in the question.
Given only the slope is missing, we cannot determine the specific points through which the line could pass. The slope is a crucial piece of information needed to calculate the equation of the line and determine the points it passes through.
A line has slope - 5/3. Through which two points could this line pass? (1 point)
Responses
(12, 13) and (17, 10)
(16, 15) and (13, 10)
(0, 7) and (3, 10)
(11, 13) and (8, 18)
To determine the two points through which a line with a slope of -5/3 could pass, we can use the slope-intercept form of a linear equation: y = mx + b.
Given the slope is -5/3, the equation in slope-intercept form becomes y = (-5/3)x + b.
To find the points, we need to solve for the y-intercept (b).
Let's plug in the coordinates of one of the given points:
(12, 13):
13 = (-5/3)(12) + b
13 = -20 + b
b = 33
Therefore, the equation becomes y = (-5/3)x + 33.
Now, let's substitute the x and y values from the other given point:
(17, 10):
10 = (-5/3)(17) + 33
10 = -85/3 + 33
To simplify, we can convert 10 into a fraction with a denominator of 3:
30/3 = -85/3 + 33
Now, we can add the fractions:
30/3 = -85/3 + 99/3
30/3 = 14/3
Since this equation is not true, (17, 10) is not a point on the line.
Therefore, the line with a slope of -5/3 could pass through the points (12, 13) and (17, 10).
The pair of points (6, y) and (10, –1) lies on a line with slope 1/4. 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 slope formula:
slope = (change in y) / (change in x)
Given that the slope is 1/4, we can set up the equation:
1/4 = (y - (-1)) / (6 - 10)
Simplifying the equation, we have:
1/4 = (y + 1) / (-4)
To solve for y, we can cross multiply:
4(y + 1) = -4
4y + 4 = -4
Subtracting 4 from both sides:
4y = -8
Dividing both sides by 4:
y = -2
Therefore, the value of y is -2.
What is the slope of the line that passes through the points (4, 2) and (4, –3)? (1 point) Responses –1 –1 0 0 1 1 undefined
To find the slope of the line that passes through the points (4, 2) and (4, -3), we can use the slope formula:
slope = (change in y) / (change in x)
In this case, the change in x is 4 - 4 = 0, which means the denominator of the slope formula is 0. However, division by 0 is undefined in mathematics.
Therefore, the slope of the line that passes through the points (4, 2) and (4, -3) is undefined.