Question

Write the equation of the line that is perpendicular to the line 3x + y = 7 and passes through the point (6, −1).

y = one thirdx − 3

y = one thirdx + 17

y = −3x − 3

y = −3x + 17

Answer 1

lets find the slope by putting your equation in y = mx + b form, where m is the slope.

3x + y = 7
y = -3x + 7
the slope of this equation is -3

are you with me so far ?

Answer 2

a perpendicular slope will have a negative reciprocal....that just means you " flip " the fraction over and change the sign......so the negative reciprocal of -3 is 1/3. That will be the slope you need.

now we will use the formula: y - y1 = m(x - x1)
using slope(m) = 1/3 and points (6,-1) -- x1 = 6 and y1 = -1

now plug our info into the formula
y - y1 = m(x - x1)
y - (-1) = 1/3(x - 6)

can you find the line now ?