Algebra.Com's Answer #548934 by MathLover1(20849)  You can put this solution on YOUR website! 1. \n" );
document.write( "Using the slope-intercept form, \n" );
document.write( " where and  \n" );
document.write( " where m=slope, b=y-intercept, \n" );
document.write( " and, substituting the values and , \n" );
document.write( " \n" );
document.write( " And the general equation is, \r \n" );
document.write( " \n" );
document.write( "\n" );
document.write( "2. \n" );
document.write( "Write the equation of a line with a slope of passing through the point (-3,-1). \r \n" );
document.write( "\n" );
document.write( "\n" );
document.write( "\n" );
document.write( " Solved by pluggable solver: FIND a line by slope and one point | \n" );
document.write( " \n" );
document.write( " What we know about the line whose equation we are trying to find out: \n" );
document.write( " \n" );
document.write( " - it goes through point (-3, -1)
\n" );
document.write( " - it has a slope of -4
\n" );
document.write( "
\n" );
document.write( " \n" );
document.write( " First, let's draw a diagram of the coordinate system with point (-3, -1) plotted with a little blue dot: \n" );
document.write( " \n" );
document.write( "  \n" );
document.write( " \n" );
document.write( " Write this down: the formula for the equation, given point and intercept a, is \n" );
document.write( " \n" );
document.write( " (see a paragraph below explaining why this formula is correct) \n" );
document.write( " \n" );
document.write( " Given that a=-4, and , we have the equation of the line: \n" );
document.write( " \n" );
document.write( "  \n" );
document.write( " \n" );
document.write( " Explanation: Why did we use formula ? 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 ( , ) lies on the line, it means that it satisfies the equation of the line. So, our equation holds for ( , ): Here, we know a, , and , and do not know b. It is easy to find out: . So, then, the equation of the line is: . \n" );
document.write( " \n" );
document.write( " Here's the graph: \n" );
document.write( " \n" );
document.write( "  \n" );
document.write( " | \n" );
document.write( " \n" );
document.write( " \n" );
document.write( " \n" );
document.write( "\n" );
document.write( "3.\r \n" );
document.write( "\n" );
document.write( "Write the equation of the line that passes through the points (2,-6) and (-2,-4). \r \n" );
document.write( "\n" );
document.write( "\n" );
document.write( "\n" );
document.write( " Solved by pluggable solver: FIND EQUATION of straight line given 2 points | \n" );
document.write( "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 . \n" );
document.write( " Intercept is found from equation , or . From that, \n" );
document.write( " intercept b is , or . \n" );
document.write( " \n" );
document.write( " y=(-0.5)x + (-5) \n" );
document.write( " \n" );
document.write( " Your graph: \n" );
document.write( " \n" );
document.write( "  \n" );
document.write( " | \n" );
document.write( " \n" );
document.write( " \n" );
document.write( " \n" );
document.write( "\n" );
document.write( "4. \n" );
document.write( "Write the equation of a line parallel to the line with a y-intercept of (0,-1).\r \n" );
document.write( "\n" );
document.write( " ...solve for first \r \n" );
document.write( "\n" );
document.write( " \r \n" );
document.write( "\n" );
document.write( " \r \n" );
document.write( "\n" );
document.write( " \r \n" );
document.write( "\n" );
document.write( "\n" );
document.write( "\n" );
document.write( " Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line | \n" );
document.write( " \n" );
document.write( " \n" );
document.write( " Since any two parallel lines have the same slope we know the slope of the unknown line is (its from the slope of which is also ).\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 \n" );
document.write( " \n" );
document.write( " Point-Slope Formula: \n" );
document.write( " \n" );
document.write( " where m is the slope and ( , ) is the given point \n" );
document.write( " \n" );
document.write( " \n" );
document.write( " \n" );
document.write( " Plug in , , and  \n" );
document.write( " \n" );
document.write( " \n" );
document.write( " \n" );
document.write( " Distribute  \n" );
document.write( " \n" );
document.write( " \n" );
document.write( " \n" );
document.write( " Multiply \n" );
document.write( " \n" );
document.write( " \n" );
document.write( " \n" );
document.write( " Subtract from both sides to isolate y \n" );
document.write( " \n" );
document.write( " Combine like terms \n" );
document.write( " \n" );
document.write( " So the equation of the line that is parallel to and goes through ( , ) is  \n" );
document.write( " \n" );
document.write( " \n" );
document.write( " So here are the graphs of the equations and  \n" );
document.write( " \n" );
document.write( " \n" );
document.write( " \n" );
document.write( " graph of the given equation (red) and graph of the line (green) that is parallel to the given graph and goes through ( , ) \n" );
document.write( " \n" );
document.write( " \n" );
document.write( " | \n" );
document.write( " \n" );
document.write( " \n" );
document.write( " \n" );
document.write( " \n" );
document.write( "\n" );
document.write( " \n" );
document.write( " |