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

Front

What does the 'm' represent in the slope-intercept form of a linear equation (y = mx + b)?

Back

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

Front

What does the 'b' represent in the slope-intercept form of a linear equation (y = mx + b)?

Back

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

Front

How do you determine if a system of equations has no solutions?

Back

If the lines represented by the equations are parallel, they will never intersect, indicating no solutions.

Front

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

Back

The slope is 2.

Front

What is the y-intercept of the line represented by the equation y = -3x + 5?

Back

The y-intercept is 5.

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

In the equation y = 4x - 2, what does the -2 represent?

Back

The initial value of y when x is 0, or the y-intercept.

Front

What does it mean for a graph to be proportional?

Back

A proportional graph passes through the origin (0,0) and has a constant ratio between y and x.

Front

If two lines intersect at one point, what can be said about the system of equations they represent?

Back

The system has one unique solution.

Front

What is the graphical representation of the equation y = 0?

Back

A horizontal line that intersects the y-axis at 0.