How to check if the points lie on the straight line ?
To check if the point (x, y) lie on the line, we have to apply the given point in the equation.
Problem 1 :
Does (3, 4) lie on the line with equation 5x + 2y = 23?
Solution:
5x + 2y = 23
Substitute x = 3 and y = 4 in the equation
5(3) + 2(4) = 23
15 + 8 = 23
23 = 23
Yes, the point lies on the equation.
Problem 2 :
Does (-1, 4) lie on the line with equation 3x - 2y = 11?
Solution:
3x - 2y = 11
Substitute x = -1 and y = 4 in the equation
3(-1) - 2(4) = 11
-3 - 8 = 11
-11 = 11
No, the point does not lies on the equation.
Problem 3 :
Does (5, -1/2) lie on the line with equation 3x + 8y = 11?
Solution:
3x + 8y = 11
Substitute x = 5 and y = -1/2 in the equation
3(5) + 8(-1/2) = 11
15 - 4 = 11
11 = 11
Yes, the point lies on the equation.
Problem 4 :
Find k if:
(2, 5) lies on the line with equation 3x - 2y = k
Solution :
3x - 2y = k
Substitute x = 2 and y = 5 in the equation
3(2) - 2(5) = k
6 - 10 = k
k = -4
Problem 5 :
Find k if:
(-1, 3) lies on the line with equation 5x + 2y = k
Solution:
5x + 2y = k
Substitute x = -1 and y = 3 in the equation
5(-1) + 2(3) = k
-5 + 6 = k
k = 1
Problem 6 :
Find a given that:
(a, 3) lies on the line with equation y = 2x - 11
Solution:
y = 2x - 11
Substitute x = a and y = 3 in the equation
3 = 2a - 11
2a = 11 + 3
2a = 14
a = 14/2
a = 7
Problem 7 :
Find a given that:
(a, -5) lies on the line with equation y = 4 - x
Solution:
y = 4 - x
Substitute x = a and y = -5 in the equation
-5 = 4 - a
-a = -5 - 4
-a = -9
a = 9
Problem 8 :
Find a given that:
(4, a) lies on the line with equation y = 1/2x + 3
Solution:
y = 1/2x + 3
Substitute x = 4 and y = a in the equation
a = 1/2 (4) + 3
a = 2 + 3
a = 5
Problem 9 :
Find a given that:
(-2, a) lies on the line with equation y = 1 - 3x
Solution:
y = 1 - 3x
Substitute x = -2 and y = a in the equation
a = 1 - 3(-2)
a = 1 + 6
a = 7
Problem 10 :
Find b if:
(2, b) lies on the line with equation x + 2y = -4
Solution:
x + 2y = -4
Substitute x = 2 and y = b in the equation
2 + 2b = -4
2b = -4 - 2
2b = -6
b = -6/2
b = -3
Problem 11 :
Find b if:
(-1, b) lies on the line with equation 3x - 4y = 6
Solution:
3x - 4y = 6
Substitute x = -1 and y = b in the equation
3(-1) - 4b = 6
-3 - 4b = 6
-4b = 6 + 3
-4b = 9
b = -9/4
Problem 12 :
Find b if:
(b, 4) lies on the line with equation 5x + 2y = 1
Solution:
5x + 2y = 1
Substitute x = b and y = 4 in the equation
5b + 2(4) = 1
5b + 8 = 1
5b = 1 - 8
5b = -7
b = -7/5
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