Perpendicular lines refers to a pair of straight lines that intercept each other. The slopes of this lines are opposite reciprocal, meaning that it's multiplication is -1.
On this case they give you the equation of a line and a point, and is asked to find the equation of a line that is perpendicular to the given one, and that passes through this point.
-2x+3y=-6 Add 2x in both sides
3y=2x-6 Divide by 3 in both sides to isolate y
y=2/3x-6/3
The slope of the given line is 2/3, which means that the slope of a line perpendicular to this one, needs to be -3/2. Now you need to find the value of b or the y-intercept by substituting the given point into the formula y=mx+b, where letter m represents the slope.
y=mx+b Substitute the given point and the previous slope found
-2=(-3/2)(6)+b Combine like terms
-2=-9+b Add 9 in both sides to isolate b
7=b
The equation that represents the line perpendicular to -2x+3y=-6 and that passes through the point (6,-2), is y=-3/2x+7.
A, Y doesn’t change and X becomes negative
Answer:
3/4 kg of sphagetti each
Step-by-step explanation:
The amount each family can take home, if the kg of sphagetti is divided equally is calculated as:
Kg of sphagetti left/Number of families
= 4 1/2kg/6
= 9/2 ÷ 6
= 9/2 × 1/6
= 9/12
= 3/4 kg
Hence, each family can take home 3/4 kg of sphagetti each.
Answer:
y⁴ - 2y²
General Formulas and Concepts:
<u>Pre-Algebra</u>
<u>Algebra I</u>
Step-by-step explanation:
<u>Step 1: Define</u>
4y⁴ - (3y² + 3y⁴) + y²
<u>Step 2: Simplify</u>
- Distribute negative: 4y⁴ - 3y² - 3y⁴ + y²
- Combine like terms (y⁴): y⁴ - 3y² + y²
- Combine like terms (y²): y⁴ - 2y²
