Question

Given the line y=3x+4 write the equation of a line in slope intercept form which is perpendicular to the given line and goes through 2,1

Answer 1

`y_{}=-(1)/(3)x+(5)/(3)`

Step-by-step explanation:

Given the line y=3x+4

Comparing it to the slope-intercept form, y=mx+b

• Slope of y=3x+4 = 3

Two lines are perpendicular if the product of their slopes is -1.

Let the slope of the new line = m

`\begin{gathered} 3m=-1 \\ m=-(1)/(3) \end{gathered}`

The slope of the perpendicular to the given line that goes through (2,1) is:

`\begin{gathered} y-y_1=m(x-x_1) \\ y-1=-(1)/(3)(x-2_{}) \end{gathered}`

We then write it in slope-intercept form.

`\begin{gathered} y_{}=-(1)/(3)x+(2)/(3)+1 \\ y_{}=-(1)/(3)x+(5)/(3) \end{gathered}`

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