6.4 standard form. 6.4 – standard form review: slope-intercept form of a linear equation is y = mx...
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6.4
Standard Form
6.4 – Standard Form
REVIEW: Slope-intercept form of a linear equation is
y = mx + b
6.4 – Standard Form
Standard Form of an equation:
Ax + By = C
where A, B, & C are REAL #s and A & B are not 0. This is a good form to graph an equation QUICKLY.
Standard Form
Ax + By = C
Rules for Standard Form:No fractionsA is not negative (it can be zero, but it
CANNOT be negative).
By the way, "integer" means no fractions, no no fractions, no decimalsdecimals. Just clean whole numbers (or their negatives).
6.4 – Standard Form
Using Standard Form, you can find the x-intercept and y-intercept, and then graph the equation.
To find the intercepts, you substitute 0 for both the x and y.
6.4 – Standard Form
Example: Find the x and y intercepts for
3x + 4y = 24.To find the x intercept, substitute 0 for the y.
3x + 4(0) = 24
3x = 24
x = 8
So, when y = 0, x = 8. Your x-int. is (8, 0).
6.4 – Standard Form
To find the y-int. substitute 0 for the x3(0) + 4y = 24
4y = 24 y = 6
So your y-int is (0, 6)Using your x and y-int, you can now
graph the equation.
6.4 – Standard Form
1 2 3 4 5–1–2–3–4–5 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
6.4 – Standard Form
Example: Graph the equation
4x + 6y = 2
1 2 3 4 5–1–2–3–4–5 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
6.4 – Standard Form
Using Standard Form, you can write equations for vertical and horizontal lines. (You can’t write vertical lines in slope-intercept form)
6.4 – Standard Form
Example: Graph the following
y= -2 x = 4When graphing these, say draw a line
through the ___ - axis at the number.
1 2 3 4 5–1–2–3–4–5 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
1 2 3 4 5–1–2–3–4–5 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
6.4 – Standard Form
If we are looking for the intercepts of an equation, standard from is the easiest to use. Therefore, we may want to change slope-intercept equations to standard form.
6.4 – Standard Form
Example: Write in Standard Form.
First we must move the xx to the other side. So we add to both sides to get:
63
2 xy
x3
2
63
2 yx
6.4 – Standard Form
Now we must make the numbers whole. So we must multiply by 33 to get rid of the fraction.
1832
63
23
yx
yx
Ex. 2: Write in standard form. )2(4
34 xy
)2(4
34 xy
4(y + 4) = 3(x – 2)
4y + 16 = 3x – 6)
Given
Multiply by 4 to get rid of the fraction.
Distributive property
4y = 3x – 22
4y – 3x= – 22
– 3x + 4y = – 22
3x – 4y = 22
Subtract 16 from both sides
Subtract 3x from both sides
Format x before y
Multiply by -1 in order to get a positive coefficient for x.
Ex. 3: Write the standard form of an equation of the line passing through (5, 4), -2/3
)5(3
24 xy
3(y - 4) = -2(x – 5)
3y – 12 = -2x +10
Given
Multiply by 3 to get rid of the fraction.
Distributive property
3y = -2x +22
3y + 2x= 22
2x + 3y = 22
Add 12 to both sides
Add 2x to both sides
Format x before y
Ex. 4: Write the standard form of an equation of the line passing through (-6, -3), -1/2
)6(2
13 xy
2(y +3) = -1(x +6)
2y + 6 = -1x – 6
Given
Multiply by 2 to get rid of the fraction
Distributive property
2y = -1x – 12
2y + 1x= -12
x + 2y = -12
Subtract 6 from both sides
Subtract 1x from both sides
Format x before y
Ex. 6: Write the standard form of an equation of the line passing through (5, 4), (6, 3)
11
1
56
43
m
)5(14 xy
First find slope of the line.
12
12
xx
yym
Substitute values and solve for m.
Put into point-slope form for conversion into Standard Form Ax + By = C
y – 4 = -1x + 5
y = -1x + 9
y + x = 9
x + y = 9
Distributive property
Add 4 to both sides.
Add 1x to both sides
Standard form requires x come before y.
Ex. 7: Write the standard form of an equation of the line passing through (-5, 1), (6, -2)
11
3
56
3
)5(6
12
m
)5(11
31 xy
First find slope of the line.
12
12
xx
yym
Substitute values and solve for m.
Put into point-slope form for conversion into Standard Form Ax + By = C
11y – 11 = -3x – 15
11y = -3x – 4
11y + 3x = -4
3x + 11y = -4
Distributive property
Add 4 to both sides.
Add 1x to both sides
Standard form requires x come before y.
11(y – 1) = -3(x + 5) Multiply by 11 to get rid of fraction
6.4 – Standard Form
Writing equations in the REAL WORLD:You are working two jobs during the
summer. You are mowing lawns and delivering newspapers. You make $12/hour mowing lawns and $5/hour delivering newspapers. If you made a total of $130, write an equation in standard form.
12x12x + + 5y5y = = 130130
6.4 – Standard Form
Example #2:You are training to participate in the
annual Ironman Championship in Kona, Hawaii. You need to burn a total of 500 calories per day to get in proper shape. Write an equation in standard form to find the minutes you would need to workout each day if you were to just swim and run.
6.4 – Standard Form
Activity Calories burned per minute
Bicycling 10
Running 11
Hiking 7
Swimming 12
Walking 2
Rowing 10