Question

Write the standard form of the equation of the line described. a) through (1,1) , parallel to y= -3x-1

Answer 1

Concept: We were told that the point (1,1) is parallel to y = -3x - 1

Let us obtain our slope from the equation given

The general form of equation of line is written in the form

`\begin{gathered} y=mx+c \\ \\ where,m=slope \end{gathered}`

Therefore,

`\begin{gathered} y=-3x-1 \\ \therefore m=-3 \end{gathered}`

Since, the point is parallel to the line given. Therefore, the slope is the same.

The formula for the equation of the line given one point is,

`y-y_1=m(x-x_1)`

Thus

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

Hence, the equation in its standard form is

`\begin{gathered} 3x+y=4 \\ \end{gathered}`