Multiple Choice
What is the slope of the line that passes through the points (–2, 5) and (1, 4)?
-3
-2
-1/3
1/3
To find the slope of a line passing through two points (x1, y1) and (x2, y2), we can use the formula:
slope = (y2 - y1) / (x2 - x1)
In this case, the two points are (-2, 5) and (1, 4). Substituting the values into the formula:
slope = (4 - 5) / (1 - (-2))
= -1 / 3
Therefore, the slope of the line passing through the points (-2, 5) and (1, 4) is -1/3.
A line has slope – 5/3 . Through which two points could this line pass?
(12, 13), (17, 10) (16, 15), (13, 10) (0, 7), (3, 10) (11, 13), (8, 18)
To determine through which two points the line with a slope of -5/3 could pass, we can use the slope-intercept form of a linear equation:
y = mx + b
where m is the slope and b is the y-intercept.
Rearranging the formula, we have:
b = y - mx
Now, we can substitute the coordinates of one of the given points into the equation to solve for b.
For the first set of points, (12, 13):
b = 13 - (-5/3)(12)
= 13 + 20
= 33
Therefore, the equation of the line passing through (12, 13) with a slope of -5/3 is:
y = -5/3x + 33
Now, let's use the equation to check the other given points:
For (17, 10):
10 = -5/3(17) + 33 -> This equation is not true.
For (16, 15):
15 = -5/3(16) + 33 -> This equation is true.
For (13, 10):
10 = -5/3(13) + 33 -> This equation is true.
For (11, 13):
13 = -5/3(11) + 33 -> This equation is true.
Therefore, the line with a slope of -5/3 could pass through the points (16, 15) and (13, 10), as well as through the points (11, 13) and (8, 18).
The pair of points (6, y) and (10, –1) lie on a line with slope the value of y?
(1 point)
–5
–2
2
5
To find the slope between two points (x1, y1) and (x2, y2), we use the formula:
slope = (y2 - y1) / (x2 - x1)
In this case, the two points are (6, y) and (10, -1). Substituting the values into the formula:
slope = (-1 - y) / (10 - 6)
= (-1 - y) / 4
Since we know that the slope is equal to 2, we can set the equation to solve for y:
2 = (-1 - y) / 4
To solve for y, we can cross-multiply:
2 * 4 = -1 - y
8 = -1 - y
To isolate y, we can subtract 1 from both sides:
8 + 1 = -y
9 = -y
Therefore, the value of y is -9.
So, the slope between the points (6, y) and (10, -1) is 2 when y = -9.