document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=534552>Question 534552</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the equation of the line that has a slope of -2 and passes through the point (1, 5) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #351582 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=351582\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are many ways to write an equation for the same line.<BR>\n" );
document.write( "A popular one is the one that starts with \"y = \" It is called the slope-intercept form and looks like<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=mx%2Bb ALIGN=MIDDLE  ALT=\"y=mx%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > with m being a number called the slope and b being a number called the y-intercept or simply intercept.<BR>\n" );
document.write( "The slope is the change in the y value divided by the corresponding change in the x value. So in a straight line with slope -2, the changes going from point (1,5) to a point (x,y), are<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1 ALIGN=MIDDLE  ALT=\"x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > for the change in x values, and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-5 ALIGN=MIDDLE  ALT=\"y-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > for the change in y values, with<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=slope=-2=%28y-5%29%2F%28x-1%29 ALIGN=MIDDLE  ALT=\"slope=-2=%28y-5%29%2F%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From that, we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-5=-2%28x-1%29 ALIGN=MIDDLE  ALT=\"y-5=-2%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That is the equation in what's called the point-slope form. You see the slope to the right of the equal sign, multiplying something in parenthesis. You see the x coordinate of the point known subtracted from x in that parenthesis. And you see the y coordinate of the point known, subtracted form y, on the left hand side.<BR>\n" );
document.write( "We can go from the point-slope form above to any other form of the equation with a little algebra.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-5=-2x%2B2%29 ALIGN=MIDDLE  ALT=\"y-5=-2x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as the first step (distributive property), and then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2x%2B7 ALIGN=MIDDLE  ALT=\"y=-2x%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" > adding 5 to both sides, takes us to the slope-intercept form.<BR>\n" );
document.write( "(I like the slope-intercept form because two equations for the same line in the slope-intercept form will always be identical, but you cannot say the same for the other forms. However, sometimes a problem specifies what form of the equation is desired, and it is good to follow instructions). </SPAN>\n" );
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