Question

Which equation in standard form has a graph that passes through the point (-3,6) and has a slope of -5/2? A. 5x + 2y = -27B. 5x + 2y = -3C. 5x + 2y = 3 D. 5x + 2y = 27

Answer 1

You need to determine an equation that passes through the point (-3,6) and has a slope of m=-5/2

To determine said equation you have to use the point slope form:

`y-y_1=m(x-x_1)`

Where

m is the slope

(x₁,y₁) are the coordinates of one point of the line.

Replace the formula with the information we have:

`\begin{gathered} y-6=-(5)/(2)(x-(-3)) \\ y-6=-(5)/(2)(x+3) \end{gathered}`

Apply the distributive probability of multiplications to the rigth side of the equation:

`\begin{gathered} y-6=-(5)/(2)\cdot x+(-(5)/(2))\cdot3 \\ y-6=-(5)/(2)x-(15)/(2) \end{gathered}`

Pass the x-related term to the left side and the constant to the rigth side of the equation

`\begin{gathered} y-6+(5)/(2)x=-(15)/(2) \\ y+(5)/(2)x=-(15)/(2)+6 \\ y+(5)/(2)x=-(3)/(2) \end{gathered}`

Multiply both sides of the equation by 2 to cancel the denominator of the fractions:

`\begin{gathered} 2(y+(5)/(2)x)=2(-(3)/(2)) \\ 2\cdot y+2\cdot(5)/(2)x=2\cdot-(3)/(2) \\ 2y+5x=-3 \end{gathered}`

Now reorder the terms to determine the standard form:

`5x+2y=-3`

The correct option is B.