What is the slope of the line that passes through the pair of points (3,8) and (9,5)?
A. -2
B. 2
C. 1/2
D. -1/2
What is the slope of the line that passes through the pair of points (-7/2, -3) and (-5, 5/2)?
A. 6/22
B. -6/22
C. 22/6
D. -22/6
Write and equation in point-slope form for the line through the given point with the given slope.
(8,3);m=5
A. y+3=5(x-8)
B. y+3=5x-8
C. y-3=5(x-8)
D. y-3=5(x+8)
To find the slope of a line that passes through two points, you can use the formula for slope:
slope = (y2 - y1) / (x2 - x1),
where (x1, y1) and (x2, y2) are the coordinates of the two points.
For the first question, the given points are (3,8) and (9,5). So, we can substitute these values into the formula to find the slope:
slope = (5 - 8) / (9 - 3) = -3 / 6 = -1/2.
Therefore, the slope of the line passing through these two points is -1/2, so the correct answer is option D.
For the second question, the given points are (-7/2, -3) and (-5, 5/2). Following the same process:
slope = (5/2 - (-3)) / (-5 - (-7/2)) = (5/2 + 6)/(-5 + 7/2) = (5/2 + 12/2) / (-5 + 14/2) = 17/2 / (-5 + 7/2) = 17/2 / (-10/2 + 7/2) = 17/2 / (-3/2) = (17/2) * (-2/3) = -34/6 = -17/3.
Therefore, the slope of the line passing through these two points is -17/3, so the correct answer is option D.
For the third question, we are given the point (8,3) and the slope m=5. The point-slope form of a linear equation is y - y1 = m(x - x1), where (x1, y1) is the given point.
Substituting the given values into the formula, we get:
y - 3 = 5(x - 8).
Expanding the equation gives:
y - 3 = 5x - 40.
Adding 3 to both sides gives the final equation:
y = 5x - 37.
Therefore, the equation in point-slope form for the line passing through the point (8,3) with slope m=5 is y = 5x - 37, so the correct answer is option B.
1. (3,8), (9,5).
m = (5-8)/(9-3) =
2. (-7/2,-3), (-5,5/2).
m = (5/2-(-3))/(-5-(-7/2)) =
(5/2+6/2)/(-10/2+7/2) =
(11/2)/(-3/2) = 11/2 * (-2/3) =
-22/6.
3. (8,3), (x,y), m = 5.
m = (y-3)/(x-8) = 5.
Cross multiply:
y-3 = 5(x-8).