document.write( "Question 904940: Write the equation of a line with a slope of and a y-intercept of (0, -2).
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\n" ); document.write( "\n" ); document.write( " Write the equation of a line with a slope of -4 passing through the point (-3,-1).
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\n" ); document.write( "\n" ); document.write( " Write the equation of the line that passes through the points (2,-6) and (-2,-4).
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\n" ); document.write( "\n" ); document.write( " Write the equation of a line parallel to the line 2x - 5y = 10 with a y-intercept of (0,-1). Write your answer in standard form.
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Algebra.Com's Answer #548934 by MathLover1(20849)\"\" \"About 
You can put this solution on YOUR website!
1.
\n" ); document.write( "Using the slope-intercept form,
\n" ); document.write( "\"y=mx%2Bb\" where \"m=slope\" and \"b=y-intercept\"
\n" ); document.write( " where m=slope, b=y-intercept,
\n" ); document.write( " and, substituting the values \"m=a\" and \"b=-2\",
\n" ); document.write( "\"y=ax-2\"
\n" ); document.write( " And the general equation is, \"ax-y-2=0+\"\r
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\n" ); document.write( "Write the equation of a line with a slope of \"-4\" passing through the point (-3,-1). \r
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Solved by pluggable solver: FIND a line by slope and one point

\n" ); document.write( " What we know about the line whose equation we are trying to find out:
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  • it goes through point (-3, -1)

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  • it has a slope of -4

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\n" ); document.write( " First, let's draw a diagram of the coordinate system with point (-3, -1) plotted with a little blue dot:
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\n" ); document.write( " Write this down: the formula for the equation, given point \"x%5B1%5D%2C+y%5B1%5D\" and intercept a, is
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\n" ); document.write( " \"y=ax+%2B+%28y%5B1%5D-a%2Ax%5B1%5D%29\" (see a paragraph below explaining why this formula is correct)
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\n" ); document.write( " Given that a=-4, and \"system%28+x%5B1%5D+=+-3%2C+y%5B1%5D+=+-1+%29+\", we have the equation of the line:
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\n" ); document.write( " \"y=-4%2Ax+%2B+-13\"
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\n" ); document.write( " Explanation: Why did we use formula \"y=ax+%2B+%28y%5B1%5D+-+a%2Ax%5B1%5D%29\" ? Explanation goes here. We are trying to find equation y=ax+b. The value of slope (a) is already given to us. We need to find b. If a point (\"x%5B1%5D\", \"y%5B1%5D\") lies on the line, it means that it satisfies the equation of the line. So, our equation holds for (\"x%5B1%5D\", \"y%5B1%5D\"): \"y%5B1%5D+=+a%2Ax%5B1%5D%2Bb\" Here, we know a, \"x%5B1%5D\", and \"y%5B1%5D\", and do not know b. It is easy to find out: \"b=y%5B1%5D-a%2Ax%5B1%5D\". So, then, the equation of the line is: \"+y=ax%2B%28y%5B1%5D-a%2Ax%5B1%5D%29+\".
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\n" ); document.write( " Here's the graph:
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\n" ); document.write( "\n" ); document.write( "Write the equation of the line that passes through the points (2,-6) and (-2,-4). \r
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Solved by pluggable solver: FIND EQUATION of straight line given 2 points
hahaWe are trying to find equation of form y=ax+b, where a is slope, and b is intercept, which passes through points (x1, y1) = (2, -6) and (x2, y2) = (-2, -4).
\n" ); document.write( " Slope a is \"a+=+%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29+=+%28-4--6%29%2F%28-2-2%29+=+-0.5\".
\n" ); document.write( " Intercept is found from equation \"a%2Ax%5B1%5D%2Bb+=+y%5B1%5D\", or \"-0.5%2A2+%2Bb+=+-5\". From that,
\n" ); document.write( " intercept b is \"b=y%5B1%5D-a%2Ax%5B1%5D\", or \"b=-6--0.5%2A2+=+-5\".
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\n" ); document.write( " y=(-0.5)x + (-5)
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\n" ); document.write( " Your graph:
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\n" ); document.write( "Write the equation of a line parallel to the line \"2x+-+5y+=+10\" with a y-intercept of (0,-1).\r
\n" ); document.write( "\n" ); document.write( "\"2x+-+5y+=+10\" ...solve for \"y\" first \r
\n" ); document.write( "\n" ); document.write( "\"2x+-+10+=+5y\"\r
\n" ); document.write( "\n" ); document.write( "\"2x%2F5+-+10%2F5+=+y\"\r
\n" ); document.write( "\n" ); document.write( "\"y=%282%2F5%29x+-+2+\" \r
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Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line

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\n" ); document.write( " Since any two parallel lines have the same slope we know the slope of the unknown line is \"0.4\" (its from the slope of \"y=0.4%2Ax-2\" which is also \"0.4\").\n" ); document.write( "Also since the unknown line goes through (0,-1), we can find the equation by plugging in this info into the point-slope formula
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\n" ); document.write( " Point-Slope Formula:
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\n" ); document.write( " \"y-y%5B1%5D=m%28x-x%5B1%5D%29\" where m is the slope and (\"x%5B1%5D\",\"y%5B1%5D\") is the given point
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\n" ); document.write( " \"y%2B1=0.4%2A%28x-0%29\" Plug in \"m=0.4\", \"x%5B1%5D=0\", and \"y%5B1%5D=-1\"
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\n" ); document.write( " \"y%2B1=0.4%2Ax-%280.4%29%280%29\" Distribute \"0.4\"
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\n" ); document.write( " \"y%2B1=0.4%2Ax-0\" Multiply
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\n" ); document.write( " \"y=0.4%2Ax-0-1\"Subtract \"-1\" from both sides to isolate y
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\n" ); document.write( " \"y=0.4%2Ax-1\" Combine like terms
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\n" ); document.write( " So the equation of the line that is parallel to \"y=0.4%2Ax-2\" and goes through (\"0\",\"-1\") is \"y=0.4%2Ax-1\"
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\n" ); document.write( " So here are the graphs of the equations \"y=0.4%2Ax-2\" and \"y=0.4%2Ax-1\"
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\n" ); document.write( " graph of the given equation \"y=0.4%2Ax-2\" (red) and graph of the line \"y=0.4%2Ax-1\"(green) that is parallel to the given graph and goes through (\"0\",\"-1\")
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