Algebra Review 1st Semester

Front

What are the characteristics of identical lines?

Back

Identical lines have the same slope and y-intercept, meaning they overlap completely.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated as m = (y2 - y1) / (x2 - x1).

Front

What does it mean for two lines to be parallel?

Back

Parallel lines have the same slope but different y-intercepts, meaning they never intersect.

Front

What does it mean for two lines to be perpendicular?

Back

Perpendicular lines have slopes that are negative reciprocals of each other, meaning their product is -1.

Front

How do you solve a system of equations graphically?

Back

To solve graphically, plot both equations on the same graph and identify the point(s) where they intersect.

Front

What is the solution to the system of equations -x + y = 1 and x + y = 1?

Back

The solution is (0, 1).

Front

How do you simplify the expression 3x⁵y⁷?

Back

The expression is already in its simplest form.

Front

What is the process to convert an equation into slope-intercept form?

Back

To convert, isolate y on one side of the equation to get it in the form y = mx + b.

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, indicating the value of y when x = 0.