word problem linear flashcard review

Front

What is an arithmetic sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. For example, in the sequence 16, 13, 10, 7, the common difference is -3.

Front

What is the explicit formula for the n^th term of an arithmetic sequence?

Back

The explicit formula for the n^th term of an arithmetic sequence can be expressed as: a_n = a₁ + (n-1)d, where a₁ is the first term and d is the common difference.

Front

How do you find the slope of a line given two points?

Back

The slope (m) of a line given two points (x₁, y₁) and (x₂, y₂) is calculated using the formula: m = (y₂ - y₁) / (x₂ - x₁).

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 write an equation of a line given a slope and a point?

Back

To write the equation of a line given a slope (m) and a point (x₀, y₀), use the point-slope form: y - y₀ = m(x - x₀).

Front

What is the y-intercept of a linear equation?

Back

The y-intercept of a linear equation is the point where the line crosses the y-axis, which occurs when x = 0. It is represented by the value of b in the slope-intercept form y = mx + b.

Front

How do you determine the equation of a line from a table of values?

Back

To determine the equation of a line from a table of values, identify the pattern in the x and y values, calculate the slope, and then use one of the points to write the equation in slope-intercept form.

Front

What is a linear equation?

Back

A linear equation is an equation that represents a straight line when graphed. It can be written in the form Ax + By = C, where A, B, and C are constants.

Front

What does it mean for a relationship to be linear?

Back

A relationship is linear if it can be represented by a straight line on a graph, indicating a constant rate of change between the variables.

Front

How do you find the cost equation from given points?

Back

To find the cost equation from given points, use the two points to calculate the slope and then use one of the points to write the equation in slope-intercept form.