Find the equation of a line through (5, -1) and...

[dieggo]

is algebra ll
i really appreciate ur help

is concerning linear equations
and it says

find the equation of a line that goes through the points (5,-1) and perpendicular to the graph of y=1/3x+1 (slope intercept form)

please help me
bye.

 

[wantedcriminal03]

I think you mean y = (x/3) + 1

The gradient ("slope") of y = (x/3) + 1 is 1/3. The gradient of the perpendicular line is the negative reciprocal of this, which is -3.

Use the formula \(\displaystyle (y\,-\,y_1)\,=\,m(x\,-\,x_1)\), where y₁ = -1 and x₁ = 5 (as given in the question), and m is the gradient.

So:

. . .\(\displaystyle y\,-\,(-1)\,=\,-3(x\,-\,5)\)
. . .\(\displaystyle y\,+\,1\,=\,-3x\,+\,15\)
. . .\(\displaystyle y\,=\,-3x\,+\,14\)