document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198769>Question 1198769</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what are the 2 points and slope for this question ? <BR>\n" );
document.write( "Connor uses a gift card to buy milkshakes for himself and his friends Thursday after he and a friend order the balance on Konners gift card was $22.45 Saturday after he and four friends ordered he had a balance of $6.70 on his  card determine the cost of each milkshake. <BR>\n" );
document.write( "I need help finding <BR>\n" );
document.write( "1 . 2 points <BR>\n" );
document.write( "2. rate of change or slope <BR>\n" );
document.write( "3. Dependent variable<BR>\n" );
document.write( "4  independent variable.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848237 by </B><A HREF=/tutors/aboutme.mpl?userid=textot><B>textot(100)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=textot><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=848237\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To analyze the situation mathematically, we can represent it as a linear relationship where the balance on the gift card decreases as the number of milkshakes purchased increases.\r<BR>\n" );
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document.write( "### Step 1: Define Variables<BR>\n" );
document.write( "- **Independent Variable**: The number of milkshakes ordered (denoted as \( x \)).<BR>\n" );
document.write( "- **Dependent Variable**: The remaining balance on the gift card (denoted as \( y \)).\r<BR>\n" );
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document.write( "---\r<BR>\n" );
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document.write( "### Step 2: Identify Two Points<BR>\n" );
document.write( "We are given:<BR>\n" );
document.write( "1. After Connor and one friend (2 milkshakes) ordered, the balance was $22.45. This gives the point \((2, 22.45)\).<BR>\n" );
document.write( "2. After Connor and four friends (5 milkshakes) ordered, the balance was $6.70. This gives the point \((5, 6.70)\).\r<BR>\n" );
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document.write( "### Step 3: Find the Rate of Change (Slope)<BR>\n" );
document.write( "The slope represents the rate at which the balance decreases per milkshake:<BR>\n" );
document.write( "\[<BR>\n" );
document.write( "m = \frac{y_2 - y_1}{x_2 - x_1}<BR>\n" );
document.write( "\]<BR>\n" );
document.write( "Substitute the points \((2, 22.45)\) and \((5, 6.70)\):<BR>\n" );
document.write( "\[<BR>\n" );
document.write( "m = \frac{6.70 - 22.45}{5 - 2} = \frac{-15.75}{3} = -5.25<BR>\n" );
document.write( "\]<BR>\n" );
document.write( "The slope is \( -5.25 \), meaning each milkshake costs **$5.25**.\r<BR>\n" );
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document.write( "---\r<BR>\n" );
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document.write( "### Step 4: Equation of the Line<BR>\n" );
document.write( "Using the point-slope form:<BR>\n" );
document.write( "\[<BR>\n" );
document.write( "y - y_1 = m(x - x_1)<BR>\n" );
document.write( "\]<BR>\n" );
document.write( "Substitute \( m = -5.25 \) and \((x_1, y_1) = (2, 22.45)\):<BR>\n" );
document.write( "\[<BR>\n" );
document.write( "y - 22.45 = -5.25(x - 2)<BR>\n" );
document.write( "\]<BR>\n" );
document.write( "Simplify:<BR>\n" );
document.write( "\[<BR>\n" );
document.write( "y = -5.25x + 10.50 + 22.45<BR>\n" );
document.write( "\]<BR>\n" );
document.write( "\[<BR>\n" );
document.write( "y = -5.25x + 32.95<BR>\n" );
document.write( "\]\r<BR>\n" );
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document.write( "---\r<BR>\n" );
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document.write( "### Step 5: Answers<BR>\n" );
document.write( "1. **Two points**: \((2, 22.45)\) and \((5, 6.70)\).<BR>\n" );
document.write( "2. **Rate of change or slope**: \( -5.25 \), meaning the cost of each milkshake is **$5.25**.<BR>\n" );
document.write( "3. **Dependent variable**: The remaining balance on the gift card (\( y \)).<BR>\n" );
document.write( "4. **Independent variable**: The number of milkshakes ordered (\( x \)).\r<BR>\n" );
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document.write( "Let me know if you'd like further clarification! </SPAN>\n" );
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