Using any two points on the line, we can find slope of the line.
Let (x_{1}, y_{1}) and (x_{2}, y_{2}) be the two points on the line.
Slope (m) = (y_{2} - y_{1}) / (x_{2} - x_{1})
Find the value of x and y so that the line through the pair of points has the given slope.
Problem 1 :
(x, 3) and (5, 9) and slope (m) = 2
Solution :
Let (x_{1}, y_{1}) ==> (x, 3) and (x_{2}, y_{2}) ==> (5, 9)
m = (9 - 3) / (5 - x)
By applying the value of m, we get
2 = 6/(5 - x)
Doing cross multiplication, we get
5 - x = 12
Subtracting 5 on both sides, we get
-x = 12 - 5
-x = 7
x = -7
So, the value of x is -7.
Problem 2 :
(-2, 3) and (4, y) and slope (m) = -3
Solution :
Let (x_{1}, y_{1}) ==> (-2, 3) and (x_{2}, y_{2}) ==> (4, y)
m = (y - 3) / (4 - (-2))
m = (y - 3) / 6
By applying the value of m, we get
-3 = (y - 3) / 6
Doing cross multiplication, we get
y - 3 = -3(6)
y - 3 = -18
Add 3 on both sides, we get
y = -18 + 3
y = -15
So, the value of y is -15.
Problem 3 :
(-3, -5) and (4, y) and slope (m) = 3
Solution :
Let (x_{1}, y_{1}) ==> (-3, -5) and (x_{2}, y_{2}) ==> (4, y)
m = (y - (-5)) / (4 - (-3))
m = (y + 5) / 7
By applying the value of m, we get
3 = (y + 5) / 7
Doing cross multiplication, we get
y + 5 = 3(7)
y + 5 = 21
Subtract 5 on both sides, we get
y = 21 - 5
y = 16
So, the value of y is 16.
Problem 4 :
(-8, -2) and (x, 2) and slope (m) = 1/2
Solution :
Let (x_{1}, y_{1}) ==> (-8, -2) and (x_{2}, y_{2}) ==> (x, 2)
m = (2 - (-2)) / (x - (-8))
m = 4 / (x + 8)
By applying the value of m, we get
1/2 = 4 / (x + 8)
Doing cross multiplication, we get
x + 8 = 4(2)
x + 8 = 8
Subtracting 8 on both sides. We get
x = 8 - 8
x = 0
So, the value of x is 0.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM