Question

Determine the equation of the line that passes through the point(-7, -1/3)and is perpendicular to the line y = - 3x – 2.Enter your answer in slope-intercept form

Answer 1

Recall that the slopes of two perpendicular lines, satisfy that:

`m_1* m_2=-1.`

Therefore, the slope of the line perpendicular to -3x-2 must-have slope

`m=(1)/(3)\text{.}`

Now, to determine the equation of the line, we will use the following formula for the equation of a line with slope m, that passes through the point (x₁,y₁):

`y-y_1=m(x-x_1)\text{.}`

Substituting (x₁,y₁)=(-7,-1/3), and m=1/3 in the above formula, we get:

`y-(-(1)/(3))=(1)/(3)(x-(-7))\text{.}`

Simplifying the above result, we get:

`y+(1)/(3)=(1)/(3)x+(7)/(3)\text{.}`

Recall that the slope-intercept form of the equation of a line is:

`y=mx+b,`

where b is the y-intercept and m is the slope.

Taking the equation of the line to its slope-intercept form we get:

`\begin{gathered} y=(1)/(3)x+(7)/(3)-(1)/(3), \\ y=(1)/(3)x+(6)/(3), \\ y=(1)/(3)x+2. \end{gathered}`

Answer:

`y=(1)/(3)x+2.`