# Points A(2,5) and B(7,8) lie on line L. What is the standard form of the equation of line L? (I got -(3/5)x-7=19/5 but it might be wrong)?

Relevance

There is disagreement over terminology, but this is how I see standard form:

ax + by = c

In this form, a should be non-negative, and all three coefficients should be integers with no common divisors, if that is possible.

The equation you give has no y term, which makes it a vertical line, and neither of the given points satisfies the equation. So yes, it might be wrong.

Here is something that works for me:

A(2, 5), B(7, 8)

(8 - 5)(x - 2) - (7 - 2)(y - 5) = 0

3(x - 2) - 5(y - 5) = 0

3x - 6 - 5y + 25 = 0

3x - 5y + 19 = 0 ... general form

3x - 5y = -19 ... standard form

• Points: (2, 5) and (7, 8)

Slope: 3/5

Equation: y = 3/5x + 19/5

• -

m = 3/5

y - 5 = (3/5) ( x - 2 )

y = (3/5) x - 6/5 + 5

y = (3/5) x + 19/5

•  - 3 x + 5 y = 19

• (5-8)x - (2-7)y = 5×7 - 2×8

-3x - (-5)y = 19

3x - 5y = -19

Source(s): The line through the points (x₁,y₁) and (x₂,y₂) in Standard Form {ax + by = c} is (y₁-y₂)x - (x₁-x₂)y = y₁x₂ - x₁y₂ before simplification.
• Anonymous
4 weeks ago

Let's use y = ax - b:

A(2, 5): 5 = a(2) - b, so b = 2a - 5

B(7, 8): 8 = a(7) - b, so 7a - 8 = b

Then 7a - 8 = 2a - 5

5a = 3

a = 3/5

Then b = 7(3/5) - 8 = 21/5 - 8 = 21/5 - 40/5 = -19/5

So y = 3/5x + 19/5