Descartes

= // Descartes // Graphing Using Slope-Intercept Form = = By: Brennen H, Jason R, and Ryan S =

Welcome to the Descartes page, where we are working on graphing using slope-intercept form. This page will tell you everything you need to know about slope-intercept form and how to use it in graphing. The first step in solving a graph using slope-intercept form, is to learn the formula. The formula for this equation would be y=mx+b; where m is the slope and the constant, and b is the y-intercept (the point where the line on the graph intercepts with the y-axis). For example, in the equation y=3x+4, the slope is 3 and the y-intercept is (0,4). //**Anything in italics is Jason's work; he couldn't log on under his own name and tell Mrs. Wilson this; Ryan, this means you. (get rid of this sentence, anything in parenthesis, and change the italics to normal phont).** There are many ways to explain this equation, but it can best be described by a table.// //The second step is to make a table.// //If you graph the points, then it will form a positive line intersecting the y-axis at (0,4) and continuing to rise two points up for every one point right, showed by this graph. (put graph).
 * //x// || //y=3x+4// || //y// || //(x,y)// ||
 * //-2// || //y=3(-2)+4// || //-2// || //(-2,-2)// ||
 * //-1// || //y=3(-1)+4// || //-1// || //(-1,1)// ||
 * //0// || //y=3(0)+4// || //0// || //(0,4)// ||
 * //1// || //y=3(1)+4// || //1// || //(1,7)// ||
 * //2// || //y=3(2)+4// || //2// || //(2,10)// ||

Word problem: A construction contracter needs to connect to build a gas station past the intersection of two highways, but north of another road heading east and west. Highway 1 goes directly north while Highway 2 slopes southwest at an angle. If the northern rise of highway 2 proportional to the eastern run of the road, shown in the equation y=2x-1, then what is the southernmost possible place the gastation can be?//

//First make your table.// //It seems that (1,2) is the answer, but it isn't very clear. Make a graph to check and make your answer clearer.
 * //x// || //y=2x-1// || //y// || //(x,y)// ||
 * //-1// || //y=2(-1)-1// || //-1// || //(-1,-3)// ||
 * //0// || //y=2(-0)-1// || //0// || //(0,-1)// ||
 * //1// || //y=3(1)-1// || //1// || //(1,2)// ||
 * //2// || //y=3(2)-1// || //2// || //(2,5)// ||
 * //3// || //y=3(3)-1// || //3// || //(3,8)// ||

The x-axis and y-axis are Highway 3 and Highway 1 respectivley. The red line shows Highway 2. Pay no attention to the green line. This graph confirmes the answer of (1,2). Your complete answer should be, "The construction contracter must build the gas station at (1,2)".//