document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=584563>Question 584563</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am having problems with x and y intercepts this problem is really getting to me. 7x+14y=10 <BR>\n" );
document.write( " I understand if you let x= 0 then the problem is just 14y=10 <BR>\n" );
document.write( " the X intercept is zero right ? <BR>\n" );
document.write( "  then i divide 10 by 14 ? its a long decimal that another site said equals to 5/7 which makes no sense to me <BR>\n" );
document.write( "please explain <BR>\n" );
document.write( "thank you  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #372828 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=372828\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's a way to think about this problem.  In an equation such as this one you are trying to graph all the coordinate pairs of points [that is (x, y) points) that are solutions to the problem. In an equation such as this one, you can choose a value for x and substitute that value into the equation and solve for the value of y that corresponds to that value of x.<BR>\n" );
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document.write( "For example, you could choose x = 3. Substitute that value of x into the equation as follows:<BR>\n" );
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document.write( "7*3 + 14y = 10<BR>\n" );
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document.write( "Multiplying the 7 times 3 makes the equation become:<BR>\n" );
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document.write( "21 + 14y = 10<BR>\n" );
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document.write( "Subtract 21 from both sides and you have:<BR>\n" );
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document.write( "14y = -11<BR>\n" );
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document.write( "Solve for y by dividing both sides by 14, and you get:<BR>\n" );
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document.write( "y = -11/14 =  -0.7857 ... rounded to 4 decimal places<BR>\n" );
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document.write( "This tells you that the coordinate point (3, -0.7857) is on the graph and is a solution to the equation.<BR>\n" );
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document.write( "This is just an example to show you what is going on when you choose values for one of the unknowns in an equation.<BR>\n" );
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document.write( "Now think of the process of graphing. Picture in your mind the origin and the horizontal x-axis and the vertical y-axis. Now picture a point on the y-axis. What has to be the corresponding value of x? Any point on the y-axis must have a corresponding value of x equal to zero. So the point where the graph crosses the y-axis (the y-intercept) can only be occur where x equals zero. <BR>\n" );
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document.write( "Just for further clarification, think of the plotting the (x, y) point (1, 2) on a coordinate system. You move from the origin to the right one unit on the x-axis and then go up 2 units above it in the y direction. This point is not on the y-axis and therefore is not the y-intercept. Similarly plot the point (-5, 8). Starting at the origin, you go 5 units to the left along the x-axis and at that point you go up 8 units in the y direction to the point (-5, 8). This is not on the y-axis either, so it cannot be the y-intercept. Now think about the plotting the (x, y) point (0, -2). You start at the origin and move neither to the left or right along the x-axis because the value of x is zero. Instead you just move down the y-axis 2 units to -2 and mark that point. Note that this point is on the y-axis and is therefore the y-intercept. This illustrates the point that I was trying to make ... whenever the value of x is zero, the corresponding value of y will be on the y-axis and therefore is the y intercept.<BR>\n" );
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document.write( "So go to the equation you were given:<BR>\n" );
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document.write( "7x + 14y = 10<BR>\n" );
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document.write( "Now choose zero for the value of x. When you set x equal to zero, 7 times zero becomes zero and the equation reduces to:<BR>\n" );
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document.write( "14y = 10<BR>\n" );
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document.write( "And you solve for y by dividing both sides by 14 to get:<BR>\n" );
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document.write( "y = 10/14 = 5/7 = 0.7143 ... rounded to four decimal places<BR>\n" );
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document.write( "This tells you that the point (0, 0.7143) is on the graph. Because x = 0 the point is on the y-axis, and therefore, 0.7143 is the y-intercept for the graph of the given equation.<BR>\n" );
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document.write( "You can just shorten the rule for doing this to say \"To find the y-intercept, set x equal to zero and solve for the corresponding value of y. That value for y will be the y-intercept ... the value where the graph crosses the y-axis.\"<BR>\n" );
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document.write( "You can use a similar line of reasoning for finding the x-intercept. Any point on the x-axis will have a corresponding y-value of zero. If y is any value other than zero, the point will be above or below the x-axis and therefore cannot be the x-intercept. The rule becomes \"To find the x-intercept, set y equal to zero and solve for the corresponding value of x. That value for x will be the x-intercept ... the value where the graph crosses the x-axis.\"<BR>\n" );
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document.write( "So go to your equation and set y equal to zero as follows:<BR>\n" );
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document.write( "7x + 14*0 = 10<BR>\n" );
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document.write( "The multiplication of 14 times zero becomes zero and you are left with:<BR>\n" );
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document.write( "7x = 10<BR>\n" );
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document.write( "Solve for x by dividing both sides by 7 to get:<BR>\n" );
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document.write( "x = 10/7 = 1&3/7 = 1.4286 ... rounded to 4 decimal places<BR>\n" );
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document.write( "So we have the (x, y) point of (1.4286, 0). This point satisfies the equation and is on the x-axis because the corresponding value of y is zero. Therefore, 1.4286 is the x-intercept. <BR>\n" );
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document.write( "In summary, the y-intercept is 0.7143 and the x-intercept is 1.4286<BR>\n" );
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document.write( "Now that you know the two intercepts, you can mark them on the coordinate system and connect them with a line through them. Then any point on that line is an (x, y) point in which the value of x and its corresponding value of y will satisfy the equation. You should get a graph that looks like this:<BR>\n" );
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document.write( "Recall way back at the beginning of this problem we worked an example using this equation, letting x = 3, and solving for y to get that the corresponding value of y is -0.7857. You can look at the graph and tell that the point (3, -0.7857 is on the graph.<BR>\n" );
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document.write( "I hope that this helps you to understand what you are doing when you set x equal to zero to find the y-intercept and when you set y equal to zero to find the x-intercept. Once you think about it and understand the concept, with a little thought and practice it should become easier. Good luck.<BR>\n" );
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