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Equation of a Line, Slope, and Y-intercept y = mx + b From Words From An Equation The interpretation of the words is very important. You know that slope, m, is the rate of change and that the yintercept, b, is the start amount. Look for word phrases that indicated change, such as, miles per hour, cost for each class, etc. This indicates the rate. If someone gives you the equation, then you can use that equation to find the slope and the intercept. Look also for words that indicate the start value. Birth, when started, etc. This indicates the y-intercept. Find these values and substitute into the equation for a line From A Table From a Graph Tables give us ordered pairs. If the relationship is linear, then all you need to do is to choose any two ordered pairs, subtract the y values, subtract the x values and write that as a ratio(fraction). Remember to put the y value on top. This is the slope. If the table includes the value when x = 0, then you have the y-intercept. If not, then go down the table until you get to x=0. This is the y intercept. Place both of these values in the equation for the line. With a graph, you need to find the rise and the run. You can do this by building a right triangle on the graph and counting the boxes or by reading the ordered pairs and finding the change in y and change in x as done in ‘From A Table’ Find the y-intercept by finding the value of y where the line crosses the y-anis. This is b. Examples From Words EX. There is 6inches of snow on the ground. The weather man predicts ½ in of snow fall per hour. From a Table (with x = 0) x y 0 1 3 3 6 5 9 7 X y 1 10 2 15 3 20 4 30 From an Equation y = 2x + 5 From a Graph