document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1210482>Question 1210482</A>: <I><SPAN STYLE=\"word-break: break-all;\"> y-8=-x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #852859 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(2138)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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/cgi-bin/show-face.mpl?user=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=852859\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ```python?code_reference&code_event_index=2<BR>\n" );
document.write( "import matplotlib.pyplot as plt<BR>\n" );
document.write( "import numpy as np\r<BR>\n" );
document.write( "\n" );
document.write( "# Define the function<BR>\n" );
document.write( "def line_function(x):<BR>\n" );
document.write( "    return -x + 8\r<BR>\n" );
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document.write( "# Generate x values<BR>\n" );
document.write( "x_values = np.linspace(-5, 10, 400)<BR>\n" );
document.write( "# Generate y values<BR>\n" );
document.write( "y_values = line_function(x_values)\r<BR>\n" );
document.write( "\n" );
document.write( "# Create the plot<BR>\n" );
document.write( "plt.figure(figsize=(8, 6))<BR>\n" );
document.write( "plt.plot(x_values, y_values, label='$y = -x + 8$')\r<BR>\n" );
document.write( "\n" );
document.write( "# Highlight the intercepts<BR>\n" );
document.write( "plt.plot(0, 8, 'ro', label='y-intercept (0, 8)')<BR>\n" );
document.write( "plt.plot(8, 0, 'go', label='x-intercept (8, 0)')\r<BR>\n" );
document.write( "\n" );
document.write( "# Add labels and title<BR>\n" );
document.write( "plt.xlabel('$x$')<BR>\n" );
document.write( "plt.ylabel('$y$')<BR>\n" );
document.write( "plt.title('Graph of $y - 8 = -x$')\r<BR>\n" );
document.write( "\n" );
document.write( "# Set grid and axes<BR>\n" );
document.write( "plt.axhline(0, color='black', linewidth=0.5)<BR>\n" );
document.write( "plt.axvline(0, color='black', linewidth=0.5)<BR>\n" );
document.write( "plt.grid(True, linestyle='--', alpha=0.6)\r<BR>\n" );
document.write( "\n" );
document.write( "# Set limits to clearly show the intercepts<BR>\n" );
document.write( "plt.xlim(-2, 10)<BR>\n" );
document.write( "plt.ylim(-2, 10)\r<BR>\n" );
document.write( "\n" );
document.write( "# Add legend<BR>\n" );
document.write( "plt.legend()\r<BR>\n" );
document.write( "\n" );
document.write( "# Save the plot<BR>\n" );
document.write( "plt.savefig('graph_y_minus_8_equals_minus_x.png')\r<BR>\n" );
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document.write( "print(\"graph_y_minus_8_equals_minus_x.png\")\r<BR>\n" );
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document.write( "```\r<BR>\n" );
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document.write( "```text?code_stdout&code_event_index=2<BR>\n" );
document.write( "graph_y_minus_8_equals_minus_x.png\r<BR>\n" );
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document.write( "```\r<BR>\n" );
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document.write( "[image-tag: code-generated-image-0-1764864400960668627]\r<BR>\n" );
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document.write( "The equation $y - 8 = -x$ can be easily graphed by rewriting it in the **slope-intercept form** ($y = mx + b$).\r<BR>\n" );
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document.write( "$$y = -x + 8$$\r<BR>\n" );
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document.write( "This line has the following key properties:\r<BR>\n" );
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document.write( "  * **Slope ($m$):** $\mathbf{-1}$ (or $\frac{-1}{1}$), meaning for every $1$ unit you move right, you move $1$ unit down.<BR>\n" );
document.write( "  * **Y-intercept ($b$):** $\mathbf{8}$, meaning the line crosses the $y$-axis at the point $(\mathbf{0, 8})$.<BR>\n" );
document.write( "  * **X-intercept:** $\mathbf{8}$, meaning the line crosses the $x$-axis at the point $(\mathbf{8, 0})$.\r<BR>\n" );
document.write( "\n" );
document.write( "The graph below shows the line $y = -x + 8$. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );