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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.

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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.



Math – graph of linear equation using a T-Chart






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Jan 26, 2013
Linear Equation
by: Staff


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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.



Math – Graphing using the Standard Form of the Equation






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Jan 26, 2013
Linear Equation
by: Staff


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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.)




Math – Graphing using the Slope-Intercept Form of the Equation













Thanks for writing.

Staff
www.solving-math-problems.com


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