document.write( "Question 1093523: What is the equation of the line that passes through the points (-1,1) and (4,7)? \n" ); document.write( "
Algebra.Com's Answer #708155 by greenestamps(13200)![]() ![]() You can put this solution on YOUR website! While most of the work in the first response you got was okay, I had a hard time following it because of the language she used. And there is an error near the end which leads to an incorrect final answer. \n" ); document.write( "I encourage you to understand what slope means, rather than blindly plugging numbers into the \"m equals y2-y1 divided by x2-x1\" formula. The slope is a measure of how fast you go up or down as you move to the right on the graph. Think of the line as a path you are hiking along; the slope is how fast you get higher or lower as you walk forward. \n" ); document.write( "So to find the slope, look at the numbers to see that you are moving from -1 to 4 in the x (\"forward\") direction, a distance of 5. In doing that, the y value changes from 1 to 7, an increase of 6. So in walking forward 5 steps, you climbed up 6 steps. Since slope is a measure of how fast you go up or down compared to how far you move forward, the slope is 6/5. \n" ); document.write( "Now one form of the equation of a line is y=mx+b, where m is the slope. We have determined that the slope is 6; we can use the x and y values of one of the points that we know are on the line to determine the value of b and thus complete the equation of the line. Using the point (x,y) = (-1,1), \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "Now we know both the slope m and the y-intercept b, so we can write the whole equation: \n" ); document.write( " |