Question

Write an equation in slope-intercept form for the line that passes through (-1,4) and perpendicular to the line y=3x+5

Answer 1

The line is perpendicular to the equation:

`y=3x+5`

So our slope will be the negative reciprocal of the slope of this line so the new slope will be:

`m=-(1)/(3)`

Now with the slope we can find the intercept in the y axis with the slope equation:

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

So we replace the slope and the coordinate, and replace x=0 to find the intercept so:

`\begin{gathered} -(1)/(3)=(y-4)/(0-(-1)) \\ y-4=-(1)/(3) \\ y=4-(1)/(3) \\ y=(11)/(3) \end{gathered}`

So the general equation will be:

`y=-(1)/(3)x+(11)/(3)`