# Graphing Calculator for Linear Equations by hedongchenchen

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```									Section 2-2: Graphing Calculator Exploration                   Name______________________
for Identifying Linear Equations

In order to graph an equation in a graphing calculator, the equation must have its y alone: “y = …”
If the y is not already isolated, you need to transform the equation so that it is alone.

Look at the following equations in a graphing calculator, one at a time. Determine which ones are linear
(make a line when graphed). Write “Yes” if it made a line or “No” if it did not next to each equation. Then,
record the locations of the x-intercepts & y-intercepts of the graphs that are lines. Once you’ve identified
equations that make lines when graphed out, think about what features of the equation could help you predict
whether the equation should make a line when you graph it or not.

To start, make sure that your WINDOW is set to STANDARD [D = {-10 < x < 10} and R = {-10 < y < 10}].
Also, note that when you want to raise x to a power (aside from “2” which can be done using a single button),
you need to use the carrot button: “^”.

1) y = 3x                               y                                 10) 3x + 2y = 12
6)    2
x                                      y
2) y = 4x2 – 10x + 1                                                      11)  2 x  1
x                                      x
7)   2
y
3) y = 4x                            8) xy = 2                            12) y = 2x + 1
y
4) y = 8                             9)    2x                            13) xy = 12 + x
x                                 14) y2 = x
5) y =     x2  1

Section 2-2: Graphing Calculator Exploration                    Name______________________
for Identifying Linear Equations

In order to graph an equation in a graphing calculator, the equation must have its y alone: “y = …”
If the y is not already isolated, you need to transform the equation so that it is alone.

Look at the following equations in a graphing calculator, one at a time. Determine which ones are linear
(make a line when graphed). Write “Yes” if it made a line or “No” if it did not next to each equation. Then,
record the locations of the x-intercepts & y-intercepts of the graphs that are lines. Once you’ve identified
equations that make lines when graphed out, think about what features of the equation could help you predict
whether the equation should make a line when you graph it or not.

To start, make sure that your WINDOW is set to STANDARD [D = {-10 < x < 10} and R = {-10 < y < 10}].
Also, note that when you want to raise x to a power (aside from “2” which can be done using a single button),
you need to use the carrot button: “^”.

1) y = 3x                             y                                10) 3x + 2y = 12
6)    2
x                                     y
2) y = 4x2 – 10x + 1                                                   11)  2 x  1
x                                     x
7)   2
y
3) y = 4x                          8) xy = 2                           12) y = 2x + 1
y
4) y = 8                           9)    2x                           13) xy = 12 + x
x
14) y2 = x
5) y =     x2  1
Once you can tell that an equation is going to make a line, you can call it a linear equation.
If the equation is linear, then there is a format called Standard Form that you should be able
to write it in.

Standard Form of a Linear Equation is Ax + By = C, where the coefficients A, B, and C are
integers and A & B aren’t both zero (though either of them could be 0), and where A isn’t
negative (p. 73). Also, A, B, & C must not have any factors in common (except for “1”).

Examples:
1) 4x + 5y = 40 is an equation in proper standard form, where A = 4, B = 5, and C = 40.

2) 3a – 7b = 42 is an equation in proper standard form, where A = 3, B = -7, and C = 42.

3) 2x = 15 may not look like it’s in standard form, but it is… 2x + 0y = 15, so A = 2, B = 0, C = 15.

4) 7y = 14 is almost in standard form… 0x + 7y = 14 should be reduced by the common factor of
7, so 0x + 1y = 2, so A = 0, B = 1, and C = 2.

5) 3x – 6y = 18 isn’t yet, but can be put in standard form…

6) ½x + ½y = 5 isn’t yet, but can be put in standard form…

7) y = 2x + 6 isn’t yet, but can be put in standard form…

Once you can tell that an equation is going to make a line, you can call it a linear equation.
If the equation is linear, then there is a format called Standard Form that you should be able
to write it in.

Standard Form of a Linear Equation is Ax + By = C, where the coefficients A, B, and C are
integers and A & B aren’t both zero (though either of them could be 0), and where A isn’t
negative (p. 73). Also, A, B, & C must not have any factors in common (except for “1”).

Examples:
1) 4x + 5y = 40 is an equation in proper standard form, where A = 4, B = 5, and C = 40.

2) 3a – 7b = 42 is an equation in proper standard form, where A = 3, B = -7, and C = 42.

3) 2x = 15 may not look like it’s in standard form, but it is… 2x + 0y = 15, so A = 2, B = 0, C = 15.

4) 7y = 14 is almost in standard form… 0x + 7y = 14 should be reduced by the common factor of
7, so 0x + 1y = 2, so A = 0, B = 1, and C = 2.

5) 3x – 6y = 18 isn’t yet, but can be put in standard form…

6) ½x + ½y = 5 isn’t yet, but can be put in standard form…

7) y = 2x + 6 isn’t yet, but can be put in standard form…

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