Regents Review Algebra

Front

What is the formula to calculate the slope of a line given two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

Find the slope of a line that passes through the points (6,3) and (1,4).

Back

The slope is m = (4 - 3) / (1 - 6) = -1/5.

Front

What is a linear regression equation?

Back

A linear regression equation is a mathematical representation of the relationship between two variables, typically in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

Using the linear regression equation, how do you predict future values?

Back

Substitute the x-value (representing time or another independent variable) into the equation to find the corresponding y-value (the predicted outcome).

Front

Find the slope of a line that passes through the points (1,1) and (3,4).

Back

The slope is m = (4 - 1) / (3 - 1) = 3/2.

Front

What is the quadratic formula used for?

Back

The quadratic formula is used to find the solutions (roots) of a quadratic equation in the form ax^2 + bx + c = 0, given by: x = (-b ± √(b² - 4ac)) / (2a).

Front

Solve the quadratic equation x^2 - 6x - 7 = 0 using the quadratic formula.

Back

The solutions are x = 7 and x = -1.

Front

What does it mean for a polynomial to be factored?

Back

Factoring a polynomial means expressing it as a product of its factors, which are polynomials of lower degrees.

Front

Which of the following is a factor of x^2 - 10x + 24?

Back

The factor is x - 4.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x = 0.