LINE SUMMARY Equations, Graphs, and Tables Slope-Intercept ...
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LINE SUMMARY Equations, Graphs, and Tables Slope-Intercept ...
Equations, Graphs, and Tables. Slope-Intercept Equation of a Line: y = ax + b
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LINE SUMMARY Equations, Graphs, and Tables Slope-Intercept Equation of a Line: y = ax + b where a is the slope and (0, b) is the vertical intercept. Generating an Equation from a Graph: 1. Pick any two points from the graph. Calculate slope (rise / run). Be careful to use correct signs. This is a. 2. Find the vertical intercept or the point where the line intersects the vertical axis. The coordinates are (0, b). 3. Substitute the values of a and b into the equation y = ax + b. Generating a Graph from an Equation: 1. Put the equation in slope-intercept form (y = ax + b) if it is not already in that form. 2. Plot the vertical intercept (0, b) on the graph. This is your starting point. 3. Convert the value of a to a fraction if it is not already in that form. (Examples: 3 would be converted to 3/1; 0.75 would be converted to 3/4.) 4. Remembering that slope is rise / run and starting from the vertical intercept, a. count up or down (depending on the sign) the number of spaces indicated by the numerator, b. then count right or left (depending on the sign) the number of spaces indicated by the denominator. [Note: The fraction -1/2 can be thought of as -1 over +2 or as +1 over -2. Either way is correct.] Generating an Equation from a Table (or Two Points): 1. Pick any two points from the table. Calculate slope [(y2 - y1) / (x2 - x1)]. Be careful to use correct signs. This is a. 2. Pick any (x, y) point from the table and, along with a, substitute these values into the slope-intercept equation (y = ax + b). 3. Solve for b. 4. Substitute the values of a and b into the equation y = ax + b. Generating a Table (or Points) from an Equation: 1. Put the equation in slope-intercept form (y = ax + b) if it is not already in that form. 2. Pick several values for x. 3. Use the equation to calculate corresponding values of y. 4. Write the x and y values in table form. Generating a Graph from a Table: 1. Plot the points and connect them with a straight line. Generating a Table from a Graph: 1. Find (x, y) points on the graph and write them in table form.
