Question

What is an equation of a line, in point-slope form, that passes through (1, – 7) and has a slope of -2/3?A. y - 7 = 2\3 (x-1)B. y + 7 = -2\3 (x-1)C. y - 7 = -2\3 (x+1)D. y + 7 = 2\3 (x+1)

Answer 1

the general equation of the line is

`y=mx+b`

where m si the slope and b an initial point , we have the slope and a point (x,y) to replace on the equation an calculate b

so

`\begin{gathered} (-7)=-(2)/(3)(1)+b \\ \\ -7=-(2)/(3)+b \\ b=-7+(2)/(3) \\ b=(-19)/(3) \end{gathered}`

then replace m and b on the general equation and we have the solution

`y=-(2)/(3)x-(19)/(3)`

this is the equation but the option have another form

on this case you can replace the point (1,-7) and check the solution, to rule out some options we know that the slope must be -2/3

so A isnt because the slope is 2/3

now check B

`\begin{gathered} y+7=-(2)/(3)(x-1) \\ (-7)+7=-(2)/(3)((1)-1) \\ 0=-(2)/(3)(0) \\ 0=0 \end{gathered}`

equality is correct

so the answer is B

we can check C because the slope is -2/3

`\begin{gathered} y-7=-(2)/(3)(x+1) \\ (-7)-7=-(2)/(3)((1)+1) \\ -14=-(2)/(3)(2) \\ -14=-(4)/(3) \end{gathered}`

the equality is wrong

this confirms that the answer is B