Algebra Class: Distance, Lines, and Sequences

What is the distance between the points A(4, 3) and B(-2, 7)?

What is the equation of the line that passes through the points (-3, 5) and (2, -1)?

What is the gradient of the line described by the equation 4x + y = 9?

What are the coordinates of the point where the line y = 3x − 4 crosses the y-axis?

What is the value of $x$ in Problem 6, where the equations are $3x + 2y = 14$ and $x - y = 1$?

Which method is primarily suggested for solving the simultaneous equations in the provided problems?

After solving Problem 7, what is the value of $y$ if the equations are $4x - 3y = 7$ and $2x + 5y = 11$?

In Problem 8, which equation is derived by substituting to isolate $x$ or $y$?

What is the next term in the sequence 3, 8, 15, 24, 35?

In Problem 6, which value of $y$ corresponds to the solution of $x = 2$?

What is the nth term of the sequence 7, 12, 17, 22, 27?

If the rule of a sequence is $T_n = 2n^2 + 3n$, what is the second term?

What is the 12th term in an arithmetic sequence where the first term is 9 and the common difference is 4?

In a geometric sequence with a first term of 5 and common ratio of 2, what is the 6th term?

What is the classification of a triangle with vertices at (0, 0), (4, 0), and (4, 3)?

Which option describes a quadrilateral formed by points (0, 0), (2, 2), (0, 2), and (2, 0)?

What is the equation of a circle with a center at (2, -3) and a radius of 5?

What method is primarily used to solve systems of linear equations in this context?

In a system of equations, what is the purpose of multiplying one or more equations?

Which of the following represents an example of solving a system of equations by elimination?

For the equations { 2x + 5y = 1, x - 7y = 2 }, what is the result when both sides of the first equation are multiplied by 3?

What is a key step involved when using the elimination method?

In Problem 8, what is the value of y after substituting the second equation into the first equation?

In Problem 9, what is the value of x after eliminating y?

What is the value of y in the solution to Problem 8?

In Problem 10, what is the value of x after solving the system of equations?

If we were to solve Problem 10 by substitution, which equation would be easiest to solve for one variable in terms of the other?