Write an equation for the line that is perpendicular to [math]n[/math] and whose [math]y[/math]-intercept is [math]\left(0,5\right)[/math]. Graph this line above.[br]
Write an equation for the line that is parallel to [math]n[/math] and that passes through the point [math]\left(3,1\right)[/math]. Graph this line above.[br]
[table][tr][td]If your teacher gives you the data card:[/td][td]If your teacher gives you the problem card:[br][/td][/tr][tr][td][list=1][*]Silently read the information on your card.[/*][*]Ask your partner, “What specific information do [br]you need?” and wait for your partner to ask for[br]information. Only give information that is on your card. [br](Do not figure out anything for your [br]partner!)[/*][*]Before telling your partner the information, ask, [br]“Why do you need to know (that piece of information)?”[/*][*]Read the problem card, and solve the problem independently.[/*][*]Share the data card, and discuss your reasoning.[/*][/list][/td][td][list=1][*]Silently read your card and think about what[br]information you need to answer the question.[/*][*]Ask your partner for the specific information that [br]you need.[/*][*]Explain to your partner how you are using the[br]information to solve the problem.[/*][*]When you have enough information, share the[br]problem card with your partner, and solve the [br]problem independently.[/*][*]Read the data card, and discuss your reasoning.[/*][/list][/td][/tr][/table]Pause here so your teacher can review your work. Ask your teacher for a new set of cards and repeat the activity, trading roles with your partner.
[size=150]Line [math]\ell[/math] is represented by the equation [math]y=\frac{2}{3}x+3[/math]. [/size][br][br]Write an equation of the line perpendicular to [math]\ell[/math], passing through [math]\left(-6,4\right)[/math]. Call this line [math]p[/math].[br]
Write an equation of the line perpendicular to [math]p[/math], passing through [math]\left(3,-2\right)[/math]. Call this line [math]n[/math].[br]
What do you notice about lines [math]\ell[/math] and [math]n[/math]? Does this always happen? Show or explain your answer.[br]
[size=150]Prove that the line [math]Ax+By=C[/math] is always perpendicular to the line that passes through [math]\left(A,B\right)[/math] and the origin.[/size]