Question

Write the standard form of the equation of the line through the given point with the given slope.

4) through: (-4,5), slope = -1/2
A) 3x+6y=-2
B) x + 2 y = 6
C) x-2y = 6
D) x-2y = -6

Answer 1

The standard form of the equation is:

`2y+x=6`

Hence, option B is true.

Explanation:

Given

• slope = m = -1/2

• point = (-4, 5)

We know the point-slope of the line equation is

`y-y_1=m\left(x-x_1\right)`

where m is the slope of the line and (x₁, y₁) is the point

substituting the values m = -1/2 and the point (-4, 5) in the point-slope form

`y-y_1=m\left(x-x_1\right)`

`y-5=(-1)/(2)\left(x-\left(-4\right)\right)`

`y-5=(-1)/(2)\left(x+4\right)`

Add 5 to both sides

`y-5+5=-(1)/(2)\left(x+4\right)+5`

`y=-(1)/(2)x+3`

Writing the equation in the standard form form

As we know that the equation in the standard form is

`Ax+By=C`

where x and y are variables and A, B and C are constants

so

`y=-(1)/(2)x+3`

`y+(1)/(2)x=3`

`2y+x=6`

Thus, the standard form of the equation is:

`2y+x=6`

Hence, option B is true.