Question

Determine the equation of the line below using the given slope and point.

Slope = m = 4 , Point (-3,-11)

Answer 1

`(\stackrel{x_1}{-3}~,~\stackrel{y_1}{-11})\hspace{10em} \stackrel{slope}{m} ~=~ 4 \\\\\\ \begin{array} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-11)}=\stackrel{m}{ 4}(x-\stackrel{x_1}{(-3)}) \implies y +11 = 4 ( x +3) \\\\\\ y+11=4x+12\implies {\Large \begin{array}{llll} y=4x+1 \end{array}}`

Answer 2

The equation is:

⇨ y + 11 = 4(x + 3)

Work/explanation:

Recall that the point slope formula is
`\rm{y-y_1=m(x-x_1)}`,

where m is the slope and (x₁, y₁) is a point on the line.

Plug in the data:

`\rm{y-(-11)=4(x-(-3)}`

Simplify.

`\rm{y+11=4(x+3)}`

Hence, the point slope equation is y + 11 = 4(x + 3).

Simplified to slope intercept:

`\rm{y+11=4x+12}`

`\rm{y=4x+1}` <- this is the simplified slope intercept equation