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Find an equation of the line passing through the pair of points. Write the equation in the form Ax+By=c?
(4,9) and (3,5)
please help
3 Answers
- techieguyLv 45 years ago
Let the general equation of a straight line be: y = mx + c ......... (this is the slope-intercept form)
Since (4, 9) is on the line:
9 = 4m + c ............................(1)
And since (3, 5) is also on the line:
5 = 3m + c ...........................(2)
Subtracting eqn. (2) from (1), we have:
9 = 4m + c
5 = 3m + c
---------------------
4 = m
Substituting the value of m in eqn. (1) and solving for c:
9 = 4*4 + c
c = 9 - 16 = -7
Substituting the values of m and c in the original equation, we get:
y = 4x - 7
y - 4x = -7
4x - y = 7
Solution: The equation of the line is 4x - y = 7
which is in the form: Ax + By = C, where A = 4, B = -1 and C = 7
- ?Lv 75 years ago
The line through (x₁,y₁) and (x₂,y₂) is given by (x₁-x₂)(y-y₂) = (y₁-y₂)(x-x₂) which can be manipulated to the standard form (y₁-y₂)x - (x₁-x₂)y = y₁x₂ - x₁y₂.
Here we have (9-5)x - (4-3)y = 9×3 - 4×5, which simplifies to 4x - y = 7
- DavidLv 75 years ago
m = (9 - 5) / (4 - 3)
m = 4
y = mx + b
9 = 4 * 4 + b
9 = 16 + b
-7 = b
y = 4x - 7
-4x + y = -7
4x - y = 7