Question

What is the point-slope form of a line with slope -4 that contains the point (-2,3)

Answer 1

`\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{3})~\hspace{10em} slope = m\implies -4 \\\\\\ \begin{array}c \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-3=-4[x-(-2)]\implies y-3=-4(x+2)`

Answer 2

Answer:
`(y-3)=(-4)(x+2)`

Explanation:

We know that the equation of a line in point-slope form that is passing through a point (a,b) and has slope m is given by :-

`(y-b)=m(x-a)`

Then, the point-slope form of a line with slope -4 that contains the point (-2,3) :-

`(y-3)=(-4)(x-(-2))\\\\\Rightarrow\ (y-3)=(-4)(x+2)`

Hence, the point-slope form of a line with slope -4 that contains the point (-2,3) is
`(y-3)=(-4)(x+2)`