2024 Rate of Change & Y-Intercept

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) where b is the y-intercept value.

Front

What does the rate of change represent in a linear function?

Back

The rate of change represents how much the y-value changes for a unit change in the x-value, often referred to as the slope of the line.

Front

How do you calculate the rate of change between two points (x1, y1) and (x2, y2)?

Back

Rate of change (slope) = (y2 - y1) / (x2 - x1).

Front

What is the slope of a line with a rate of change of -6/4?

Back

The slope is -6/4, which can be simplified to -3/2.

Front

If a line has a slope of 4/3, what does this indicate about the line's steepness?

Back

A slope of 4/3 indicates that for every 3 units moved horizontally, the line rises 4 units vertically, making it a steep line.

Front

What is the significance of a positive slope?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, showing a direct relationship.

Front

What does a negative slope indicate about the relationship between x and y?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, showing an inverse relationship.

Front

What is the y-intercept of the line represented by the equation y = 2x - 1?

Back

The y-intercept is -1, which is the value of y when x = 0.

Front

How can you identify the y-intercept from a graph?

Back

The y-intercept can be identified as the point where the line crosses the y-axis.

Front

What is the formula for 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.