Question

What is the equation of the line in slope-intercept form? the line perpendicular to

y = 1/3x + 5 through (2, 1)
A. y = -1/3x + 7

B. y = 3x + 7
C. y = -3x + 7
D. y = 1/3x + 7

Answer 1

\[\large y = \frac{1}{3}x + 5\]

This is the line we have....to find a line perpendicular to it...we first know the the slope of our new line would be the negative reciprocal of this lines slope..

*also known as...when you multiply the slope we get...and the slope we have...you get -1*

So

Negative = \(\large -\frac{1}{3}\) reciprocal = flip so \(\large -\frac{3}{1} = -3\)

This is our new slope...and look we have a point...(2,1)

Hmm slope, point? looks like we can use the point slope formula

\[\large y - y_o = m(x - x_0)\]

replace \(\large m\) with -3 , \(\large y_o\) with 1 , and \(\large x_o\) with 2

\[\large y - 1 = -3(x - 2)\]
Distribute this out
\[\large y - 1 = -3x + 6\]
And add 1 to both sides of the equation
\[\large y = -3x + 7\]

This would be our equation :)

Answer 2

What is the equation of the absolute value function?

Answer 3

@johnweldon1993

Answer 4

Do you have choices?