Acellus Algebra 2 - Linear Equations Quiz

Equations of Lines: Slope-Intercept Form

• The relationship between x and y can be represented in the form y = mx + b, where m is the slope and b is the y-intercept.
• For the dataset {X: -1, 0, 1, 2, 3, 4, 5} and {Y: -2, 3, 8, 13, 18, 23, 28}, the equation is Y = 5x + 3.
• For {X: 0, 1, 2, 3, 4} and {Y: -1, 3, 7, 11, 15}, the equation becomes y = 4x - 1.
• For {X: 0, 1, 2, 3, 4, 5} and {Y: 1, -1, -3, -5, -7, -9}, the equation is Y = -2x + 1.
• Given the relationship {X: -2, -1, 0, 1, 2, 3} and {Y: -4, -2, 0, 2, 4, 6}, the equation simplifies to y = 2x.
• For the dataset {X: 0, 1, 2, 3, 4, 5} and {Y: 7, 9, 11, 13, 15, 17}, the equation is y = 2x + 7.
• For {X: 0, 1, 2, 3, 4, 5, 6} and {Y: 5, 6, 7, 8, 9, 10, 11}, the equation is y = x + 5.
• Given {X: 1, 2, 3, 4, 5, 6} and {Y: -4, -3, -2, -1, 0, 1}, the resulting equation is y = x - 5.

Combining and Simplifying Expressions

• Combining like terms: 8y - 4z + 3y + 5z simplifies to 11y + z.
• Using the distributive property with 3(4x - 9) results in 12x - 27.
• Combining terms 9y + 5y - 3 simplifies to 14y - 3.
• The expression 3x - 7x simplifies to -4x.
• Distributing 4(5x + 3y - 7) results in 20x + 12y - 28.
• For 6(3x - 4y + 7z), results are 18x - 24y + 42z.
• Combining 4x - 7y + 2x - 4 gives 6x - 7y - 4.

Evaluating Expressions

• Evaluating 4a - 2(a + b) + 1 with a = 2 and b = 4 yields -3.
• For x = 1 and y = 2, the expression evaluates to 23.
• Simplifying 3b - 2(1 - b) / a - 2 using a = 3 and b = 2 gives 8.
• Evaluating 20a - 1 / b with a = 2 and b = 13 results in 3.
• When m = 25, the expression m + 2(m - 5) evaluates to 65.
• For x = 14 and y = 1/3, the expression 2x / 13 - 9y evaluates to 14/5, or 2.8.
• Evaluating 4a + 2b^2 - 2(a - 3b) with a = 2 and b = 4 results in 60.

Solving Equations

• Solving the equation -4(3 + x) + 5 = 4(x + 3) results in x = -19/8.
• From -2(4 + 3x) = 3(x - 2), x simplifies to -2/9.
• The equation 4(x + 5) = 6(2x - 1) gives x = 13/4.
• In 3(x - 2) + 6 = 4(2 - x), x equals 8/7.
• Solving -(x - 1) + 10 = -3(x - 2) leads to x = -5/2.
• The equation 10x - 2(x + 5) = 4x - 2 results in x = 2.
• For 5x - (x + 3) = 3(2 - 2x) + x, x simplifies to 1.

Analyzing Zero Solutions and Inequalities

• The condition 0 = -4 can imply specific values of x when paired with factors like -7/3 and 5.
• Inequalities such as 4 suggest solutions could fall into specific ranges.