Graphing Equations

Front

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

Back

The slope-intercept form of a linear equation is given by y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you identify the slope and y-intercept from the equation y = 0.5x - 2?

Back

In the equation y = 0.5x - 2, the slope (m) is 0.5 and the y-intercept (b) is -2.

Front

What does the graph of y = |x| look like?

Back

The graph of y = |x| is a V-shaped graph that opens upwards, with the vertex at the origin (0,0).

Front

How do you graph the equation y = -3x + 5?

Back

To graph y = -3x + 5, plot the y-intercept (0,5) and use the slope of -3 to find another point, then draw a straight line through these points.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the steepness of the line and the direction of the relationship between the variables; a positive slope means the line rises, while a negative slope means it falls.

Front

What type of graph does the equation y = 3^x produce?

Back

The equation y = 3^x produces an exponential curve that increases rapidly as x increases.

Front

What is the y-intercept of the equation y = 4x + 2?

Back

The y-intercept of the equation y = 4x + 2 is 2, which is the point where the line crosses the y-axis.

Front

How can you determine if a linear equation is increasing or decreasing?

Back

A linear equation is increasing if the slope is positive and decreasing if the slope is negative.

Front

What are the key characteristics of a linear function?

Back

A linear function has a constant rate of change, can be represented by a straight line, and is defined by the equation y = mx + b.

Front

What does the term 'exponential growth' refer to in graphing?

Back

Exponential growth refers to a situation where a quantity increases at a rate proportional to its current value, resulting in a rapid increase over time.