y = mx + b, interpreting m and b, and systems of equations

Front

What does the equation y = mx + b represent?

Back

It represents a linear equation where 'm' is the slope and 'b' is the y-intercept.

Front

In the equation y = mx + b, what does 'm' represent?

Back

The slope of the line, indicating the rate of change of y with respect to x.

Front

In the equation y = mx + b, what does 'b' represent?

Back

The y-intercept, which is the value of y when x = 0.

Front

What is the slope of the line represented by the equation y = 2x + 3?

Back

The slope is 2.

Front

If a line has a slope of -1, what does this indicate about the line's direction?

Back

The line decreases as it moves from left to right.

Front

What does it mean for two lines to be parallel in terms of their slopes?

Back

Parallel lines have the same slope.

Front

What is the solution to the system of equations: y = 2x + 1 and y = -x + 4?

Back

The solution is (1, 3).

Front

How do you determine if a point is a solution to a system of equations?

Back

Substitute the point's coordinates into both equations; if both equations are true, it's a solution.

Front

What does it mean if a system of equations has no solution?

Back

The lines are parallel and do not intersect.

Front

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

Back

The lines are the same, meaning they overlap completely.