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.

Front

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

Back

The explicit formula is given by 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) is calculated using the formula m = (y₂ - y₁) / (x₂ - x₁), where (x₁, y₁) and (x₂, y₂) are the two points.

Front

What is 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.

Front

What does it mean for a line to have a slope of 0?

Back

A line with a slope of 0 is horizontal and indicates that the y-value remains constant regardless of the x-value.

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of y when x = 0.

Front

How do you write the equation of a line given the slope and a point?

Back

Use the point-slope form: y - y₁ = m(x - x₁), where (x₁, y₁) is the point and m is the slope.

Front

What is the formula for finding the y-value of a line at a specific x-value?

Back

Substitute the x-value into the equation of the line (y = mx + b) to find the corresponding y-value.

Front

What is the relationship between the slope and the angle of a line?

Back

The slope of a line is the tangent of the angle (θ) it makes with the positive x-axis: m = tan(θ).

Front

How do you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope (m) and different y-intercepts (b).