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 = -3x + 7


B. y = 1/3x + 7



C. y = -1/3x + 7



D. y = 3x + 7

Answer 1

what the slope of -> y = 1/3x + 5 ?

Answer 2

So, we know that for a function to be perpendicular to another, their slopes have to opposite and reciprocal ( which means that they must be the opposite sign, and raised to the -1 power [just put the slope in the denominator]).

Answer 3

I would love to walk this with you step by step, but i g2g...sorry.

Answer 4

@alexwright it's time for you to respond if you want some help...

Answer 5

sorry @whpalmer4 I don't know what to do on this question that's why im asking

Answer 6

would it be C since it is opposite? @JonnyVonny

Answer 7

is the slope (2,1) @whpalmer4

Answer 8

No, (2,1) is the point the line goes through.

\[y = \frac{1}{3}x+5\]That's slope-intercept form, from which you can "read off" the slope directly.

\[y = mx+b\]\(m\) is the slope, \(b\) is the value of the y-intercept

Answer 9

so which one would that be? @whpalmer4

Answer 10

what is the slope of the line described by \[y = \frac{1}{3}x+5\]If you can't figure that out, you're not going to get anywhere with this problem (or many others). I've given you all the information you need...

Answer 11

Compare the two equations:

\[y = \frac{1}{3}x+5\]\[y=mx+b\]What is the value of \(b\) if they are equal? What is the value of \(m\) if they are equal?

Answer 12

Having found the value of \(m\), the slope of the existing line, you can find the value of the slope of the perpendicular line: \(-1/m\) because the slopes of perpendicular lines have a product of \(-1\) (unless they are the special case of lines parallel to the x and y axes, which is not the case here).

Finally, you need to use the point-slope formula to construct the equation of the line that has your new slope (which I will confusingly again call \(m\)) and passes through the point \((x_1,y_1) = (2,1)\):

\[y-y_1 = m(x-x_1)\]

After doing that, rearrange into the form of the answers by solving for \(y\).