Question

Through: (5,-1), perp. to y =1/3x+2

Answer 1

Answer: y = -3x + 14

Step-by-step explanation

The given line is of the form y = mx+b

• m = 1/3 = slope
• b = 2 = y intercept

Flip the fraction and flip the sign of 1/3 to get to -3/1 aka -3. This is the negative reciprocal.

Now let's apply point-slope form.

`\text{y}-\text{y}_1 = \text{m}(\text{x}-\text{x}_1)\\\\\text{y}-(-1) = -3(\text{x}-5)\\\\\text{y}+1 = -3\text{x}+15\\\\\text{y} = -3\text{x}+15-1\\\\\text{y} = -3\text{x}+14\\\\`

As a check, plugging x = 5 into the answer y = -3x+14 should get you the output y = -1. I'll let the student do this check.