Question

ASSIGNMENT PointWhich of the following equations represent a linethat has a slope of -5 and that passes through (2,-6)? Check all of the boxes that apply.Oy+6=-5(x-2)y-2=-5(x + 6)y = -5x +4y=-5x-28DONE

Answer 1

Step-by-step explanation

We are given the following:

We are required to determine the equations that have a slope of -5 and passes through (2, -6).

We know that the slope-intercept form of a straight line is given as:

`\begin{gathered} y=mx+b \\ where \\ m=slope \\ b=y\text{ }intercept \end{gathered}`

We can determine the given equations as follows:

`\begin{gathered} \Rightarrow y+6=-5(x-2) \\ Simplifying,we\text{ }have \\ y+6=-5x+10 \\ y=-5x+10-6 \\ y=-5x+4 \\ slope=-5 \\ Testing\text{ }the\text{ }point\text{ }(2,-6) \\ -6=-5(2)+4 \\ -6=-6 \\ \\ \Rightarrow y-2=-5(x+6) \\ Upon\text{ }simplification \\ y-2=-5x-30 \\ y=-5x-30+2 \\ y=-5x-28 \\ slope=-5 \\ Testing\text{ }the\text{ }point\text{ }(2,-6) \\ -6=-5(2)-28 \\ -6=-38 \end{gathered}`
`\begin{gathered} \Rightarrow y=-5x+4 \\ slope=-5 \\ Test\imaginaryI ng\text{ t}he\text{ p}o\imaginaryI nt\text{ \lparen}2,-6) \\ -6=-5(2)+4 \\ -6=-6 \\ \\ \Rightarrow y=-5x-28 \\ slope=-5 \\ Test\imaginaryI ng\text{ t}he\text{ p}o\imaginaryI nt\text{ \lparen}2,-6) \\ -6=-5(2)-28 \\ -6=-38 \end{gathered}`

Hence, the answers are:

`\begin{gathered} y+6=-5(x-2) \\ \\ y=-5x+4 \end{gathered}`