# Graphing a Linear Equation

Graphing a Linear Equation

How do I graph the line given by the equation y = 2x – 5?

Show how to plot this equation (1) using a T-Chart (table of values), (2) using the standard form of the equation, and using (3) slope-intercept technique.

### Comments for Graphing a Linear Equation

 Jan 26, 2013 Linear Equation by: Staff Answer Part I (1) Graphing using a “T-Chart” A “T-Chart” is a table of values which can be plotted directly on an x-y coordinate grid. Once the points are plotted, draw a straight line through the points. The equation is: y = 2x – 5 Arbitrarily pick several values of x (to be safe, choose at least 3), and then compute the corresponding y value. Record these values in the “T-Chart” format.  x                  y = 2x – 5 ---           ----------------------------  0              y = 2*0 – 5 = -5  1              y = 2*1 – 5 = -3  2              y = 2*2 – 5 = -1  3              y = 2*3 – 5 = 1  x              y ----           -----  0             -5  1             -3  2             -1  3              1 Plot all four points on an x-y corrdinate system, and then draw a straight line through the points. -----------------------------------------------------

 Jan 26, 2013 Linear Equation by: Staff ----------------------------------------------------- Part II (2) Graphing using the “Standard Form of the Equation” The equation given in the problem statement is written in the slope-intercept format: y = mx + b To graph this equation using the standard form of the equation, the equation must be rewritten in the following format: Ax + By = C y = 2x - 5 y - y = 2x - 5 - y 0 = 2x - 5 - y 0 = 2x - y - 5 0 + 5 = 2x - y - 5 + 5 5 = 2x - y - 5 + 5 5 = 2x - y + 0 5 = 2x - y 2x - y = 5 Compute the coordinates of the following two points: If x = 0, what is the y value? 2x - y = 5 2 * 0 - y = 5 0 - y = 5 - y = 5 y = - 5 the x-y coordinates for this point are: (0,-5) If y = 0, what is the x value? 2x - y = 5 2x - 0 = 5 2x = 5 2x / 2 = 5 / 2 x * (2 / 2) = 5 / 2 x * (1) = 5 / 2 x = 5 / 2 x = 2.5 the x-y coordinates for this point are: (2.5,0) Plot these two points on an x-y corrdinate system, and then draw a straight line through the points. -----------------------------------------------------

 Jan 26, 2013 Linear Equation by: Staff ----------------------------------------------------- Part III (3) Graphing using the “Slope-Intercept Form of the Equation” The problem statement gives the equation in slope-intercept form: y = mx + b m = slope of the straight line b = y-intercept for your equation: y = 2x - 5 m = 2 b = -5 Plot the y-intercept (b = -5) an x-y corrdinate system. Draw a straight line with a slope of m (m = 2) through y-intercept. m = slope = “rise” over “run”, or “rise” DIVIDED BY “run” m = slope = (change in “y” values)/(change in “x” values) m = 2 (each time the value of x increases by 1, the value of y increases by 2; or when x increases by 2, y increases by 4, and so on. The value of y increases twice as fast as the value of x.) Thanks for writing. Staff www.solving-math-problems.com