Enter in standard form the equation of the line passing through the given point and having the given slope. B(2, - 5), m = -2/3

Answer 1

Answer: 2x+3y=-11

We are given one point on the line (2,-5) and the slope m=-2/3. Using the formula y-y₁=m(x-x₁) we can identify the equation of the line if y₁=-5 and x₁=2 and plugging them in.

y--5=-2/3(x-2) Subtracting a negative becomes positive. Distribute -2/3.

y+5=-2/3x+4/3

Now we have an equation, but it needs to be in standard form. The formula for standard form is Ax+By=C.

We need to get x and y on the same side.

y+5=-2/3x+4/3 Subtract 5 to the other side

y=-2/3x-11/3 Add 2/3x to the other side

2/3x+y=-11/3 In standard form, we cannot have fractions. Multiply everything by 3 to cancel the fraction.

3(2/3x+y=-11/3)

2x+3y=-11 This is the equation of the line in standard form.