DCP Brain Dump #2

Front

What is a system of equations?

Back

A set of two or more equations with the same variables. Solutions are the values that satisfy all equations simultaneously.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

It means that there are an infinite number of points that satisfy all equations in the system, often indicating that the equations represent the same line.

Front

How do you find the slope of a line given two points?

Back

Use the formula: slope (m) = (y2 - y1) / (x2 - x1).

Front

What is the slope of a line that rises 4 units for every 5 units it runs?

Back

The slope is 4/5.

Front

What is the rate of change in a linear equation?

Back

The rate of change is the slope of the line, indicating how much y changes for a change in x.

Front

How do you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope and will never intersect.

Front

What is the formula for the slope between two points (x1, y1) and (x2, y2)?

Back

The formula is m = (y2 - y1) / (x2 - x1).

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as x increases, y decreases, meaning the line falls from left to right.

Front

What are perpendicular lines?

Back

Perpendicular lines are lines that intersect at a right angle (90 degrees). Their slopes are negative reciprocals of each other.

Front

Back

The slope is -3.