Answer:
Step-by-step explanation:
The equation being shown in the question is the absolute value of x. Absolute values when graphed show up as a V-shaped graph pointing upwards. This is because whatever value is passed as an input will output a positive, regardless of whether the input is positive or negative. Meaning that both 4 and -4 will output 4. That is why the graph is a V-shaped because the outputs repeat for both positive and negative inputs. In this case since the negative is outside the absolute value brackets the positive value given from the absolute value of the input will be turned into a negative. So this will cause the V-shape graph to be reflected across the x-axis. As seen in the attached picture below.
1. 3rd one
2. f(x) = 7x - 5
f(2) = 7(2) - 5
f(2) = 14 - 5
f(2) = 9
3. c(n) = 0.75n - 0.25
4. (0,0)(2,4)
slope = (4 - 0) / (2 - 0) = 4/2 = 2
answer is : y = 2x
Answer:
(-19, 55)
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
<u>Algebra I</u>
- Solving systems of equations using substitution/elimination
Step-by-step explanation:
<u>Step 1: Define Systems</u>
y = -3x - 2
5x + 2y = 15
<u>Step 2: Solve for </u><em><u>x</u></em>
<em>Substitution</em>
- Substitute in <em>y</em>: 5x + 2(-3x - 2) = 15
- Distribute 2: 5x - 6x - 4 = 15
- Combine like terms: -x - 4 = 15
- Isolate <em>x</em> term: -x = 19
- Isolate <em>x</em>: x = -19
<u>Step 3: Solve for </u><em><u>y</u></em>
- Define original equation: y = -3x - 2
- Substitute in <em>x</em>: y = -3(-19) - 2
- Multiply: y = 57 - 2
- Subtract: y = 55
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Answer:
y= -5x +24
Step-by-step explanation:
<u>Slope-intercept form</u>
y= mx +c, where m is the slope and c is the y-intercept.
Given that the slope is -5, m= -5.
Substitute m= -5 into the equation:
y= -5x +c
To find the value of c, substitute a pair of coordinates that the line passes through into the equation:
When x= 3, y= 9,
9= -5(3) +c
9= -15 +c
c= 9 +15
c= 24
Thus, the equation of the line is y= -5x +24.