7.4A & 7.7A Constant Rate of Change & Linear Relationships

Front

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

Back

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

Front

Define 'constant rate of change'.

Back

A constant rate of change refers to a situation where the change in one quantity is consistent with the change in another quantity, often represented as the slope in a linear relationship.

Front

What does the slope of a line represent in a graph?

Back

The slope represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how much y changes for a unit change in x.

Front

How do you find the slope from two points (x1, y1) and (x2, y2)?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the value of y when x is 0, represented by the 'b' in the slope-intercept form y = mx + b.

Front

Write the equation of a line with a slope of 3 and a y-intercept of 2 in slope-intercept form.

Back

The equation is y = 3x + 2.

Front

What is the constant rate of change if a line passes through the points (1, 4) and (3, 10)?

Back

The constant rate of change (slope) is 3, calculated as (10 - 4) / (3 - 1).

Front

If a line has a slope of -2, what does this indicate about the relationship between x and y?

Back

A slope of -2 indicates that for every 1 unit increase in x, y decreases by 2 units, showing an inverse relationship.

Front

What is the equation of a line that passes through the point (0, 5) and has a slope of -1?

Back

The equation is y = -1x + 5.

Front

How can you determine if a relationship is linear from a table of values?

Back

A relationship is linear if the rate of change between the values is constant.