1. Answer: [tex]y=\dfrac{3}{4}x-3[/tex] [tex]m=\dfrac{3}{4}[/tex] [tex]b=-3[/tex]
Step-by-step explanation:
The slope-Intercept form is: y = mx + b
- m is the slope
- b is the y-intercept
3x - 4y = 12
-4y = -3x + 12 subtracted 3x from both sides
[tex]\dfrac{-4}{-4}y=\dfrac{-3}{-4}x+\dfrac{12}{-4}[/tex] divided both sides by -4
[tex]y=\dfrac{3}{4}x-3[/tex]
- m = [tex]\dfrac{3}{4}[/tex]
- b = -3
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2. Answer: [tex]y=\dfrac{1}{3}x-5[/tex] [tex]m=\dfrac{1}{3}[/tex] [tex]b=-5[/tex]
Step-by-step explanation:
The slope-Intercept form is: y = mx + b
- m is the slope
- b is the y-intercept
x - 3y = 15
-3y = -x + 15 subtracted x from both sides
[tex]\dfrac{-3}{-3}y=\dfrac{-1}{-3}x+\dfrac{15}{-3}[/tex] divided both sides by -3
[tex]y=\dfrac{1}{3}x-5[/tex]
- m = [tex]\dfrac{1}{3}[/tex]
- b = -5
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3. Answer: y = -5x + 9 m = -5 b = 9
Step-by-step explanation:
The slope-Intercept form is: y = mx + b
- m is the slope
- b is the y-intercept
5x + 2y = y + 9
5x + y = 9 subtracted y from both sides
y = -5x + 9 subtracted x from both sides
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4. Answer: [tex]x=-\dfrac{5}{7}[/tex] [tex]x=3[/tex]
Step-by-step explanation:
To solve an absolute value equation:
- isolate the absolute value expression
- split the equation into 2 equations (one positive and one negative)
- solve for each equation
- NOTE: absolute value expression cannot be equal to a negative
| 7x - 8 | = 13 isolated absolute value expression is equal to a positive
-(7x - 8) = 13 +(7x - 8) = 13 separated into 2 equations
7x - 8 = -13 7x - 8 = 13 divided by the +/- sign
7x = -5 7x = 21 added 8 to both sides
x = [tex]-\dfrac{5}{7}[/tex] x = 3 divided both sides by 7
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5. Answer: x = -9 x = -2
Step-by-step explanation:
To solve an absolute value equation:
- isolate the absolute value expression
- split the equation into 2 equations (one positive and one negative)
- solve for each equation
- NOTE: absolute value expression cannot be equal to a negative
3| 2x + 11 | = 21 need to divide both sides by 3
| 2x + 11 | = 7 isolated absolute value expression is equal to a positive
-(2x + 11) = 7 +(2x + 11) = 7 separated into 2 equations
2x + 11 = -7 2x + 11 = 7 divided by the +/- sign
2x = -18 2x = -4 subtracted 11 from both sides
x = -9 x = -2 divided both sides by 2
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6. Answer: No solution
Step-by-step explanation:
To solve an absolute value equation:
- isolate the absolute value expression
- split the equation into 2 equations (one positive and one negative)
- solve for each equation
- NOTE: absolute value expression cannot be equal to a negative
-2| x + 7 | - 3 = 13 need to add 3 to both sides
-2| x + 7 | = 16 need to divide both sides by -2
| x + 7 | = -8 isolated absolute value expression is equal to a negative
It is not possible for a positive (absolute value) to be equal to a negative so there is no solution.
