Can anyone check if I got this right?

http://prntscr.com/bkmnxd

Question

Can anyone check if I got this right?

http://prntscr.com/bkmnxd

whpalmer4 · Answer

Nope, sorry, incorrect.

You are graphing lines, which only have single powers of the independent variable, but your answers have higher powers of the independent variable.

whpalmer4 · Answer

You could also have checked this yourself by making a table of values with your answer equation and graphing them to see if they all fall on the desired lines...

whpalmer4 · Answer

Do you want to work through the problem with me?

mathguy5 · Answer

Yes,please.

whpalmer4 · Answer

Okay, so we know we want to make a line that is perpendicular to the line given by $y = 2x$, right?  What is the relationship between the slopes of two lines which are perpendicular (assuming not parallel to x/y axes)?

mathguy5 · Answer

Theyre the same I think.

whpalmer4 · Answer

no, that would parallel lines.  Look at the picture, do both of those lines have the same slope?  Remember, slope is the amount you go up (or down) with each unit you move to the right.  Positive slope means you go up as you go to the right, negative slope means you go down as you go to the right, and 0 slope means it is level.

whpalmer4 · Answer

The relationship of the slopes of two perpendicular lines is that the product of the slopes is equal to -1 (again, assuming the lines in question are not parallel to the x and y axes).

What is the slope of the line given by $y = 2x$?

mathguy5 · Answer

2

whpalmer4 · Answer

Right.  So if we have two numbers which when we multiply them together give us a product of $-1$, and one of the numbers is $2$, what must the other number be?

mathguy5 · Answer

I think I got it now. The slope intercept form is y=2x and the point slope is the same right?

mathguy5 · Answer

Was I correct?

whpalmer4 · Answer

slope intercept form is $$y = mx+b$$ where $m$ is the slope and $b$ is the y-intercept (the value of $y$ when $x=0$)

point-slope form is $$y-y_0 = m(x-x_0)$$where $(x_0,y_0)$ is a point that the line goes through, and $m$ is the slope

whpalmer4 · Answer

slope intercept form of the original line is $y = 2x$ 
which means $m=2$ and $b=0$

but we need to find the equation for a line which is perpendicular to that line.

If we have two perpendicular lines, one with slope $m_1$ and the other slope $m_2$, then we will have $m_1 *m_2 = -1$

We have $m_1=2$ here.  What is $m_2=$?

mathguy5 · Answer

-0.5? ince -0.5X2=-1 ?

whpalmer4 · Answer

yes, though I would write it as -1/2 rather than -0.5

whpalmer4 · Answer

so our perpendicular line will have slope $m = -1/2$  but we also have to make the equation so that the line goes through the point $(-1,-2)$ as shown on the diagram

for that, we'll use the point-slope formula, which allows us to construct the equation if we know the slope (we do) and a point on the line (we do)

whpalmer4 · Answer

Give it a try and tell me what you get...

mathguy5 · Answer

y=1/2x-5/2

mathguy5 · Answer

Is that right?

whpalmer4 · Answer

no, not correct.  

look, we have our known point of $(-1,-2)$ and our slope of $m=-1/2$

point-slope formula is $$y-y_0 = m(x-x_0)$$fill in the blanks:

$$y-(-2) = -\frac{1}{2}  (x-(-1))$$Simplify that and you get
$$y+2 = -\frac{1}{2}(x+1)$$
That is your equation for the perpendicular line in point-slope form.

To get slope-intercept form, you just rearrange that equation so you only have $y$ on the left-hand side, and use the distributive property to get rid of the parentheses.

whpalmer4 · Answer

@mathguy5