word problem linear flashcard review

Front

Identify the slope and y-intercept in the equation: y = mx + b

Back

Slope (m) is the coefficient of x, and y-intercept (b) is the constant term. For y = 2x + 4, slope = 2, y-intercept = 4.

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

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

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Front

What does a slope of 0 indicate about a line?

Back

A slope of 0 indicates a horizontal line.

Front

What is the equation of a line with a slope of -1 that passes through the point (3, 4)?

Back

Using point-slope form: y - 4 = -1(x - 3) simplifies to y = -x + 7.

Front

If a line has a slope of 2 and passes through the point (0, 4), what is its equation?

Back

Using slope-intercept form: y = 2x + 4.

Front

What is the meaning of the y-intercept in a real-world context?

Back

The y-intercept represents the starting value of a situation when x = 0.

Front

How do you write a linear equation from a word problem?

Back

Identify the variables, set up the equation based on the relationship described, and solve for the unknown.

Front

If Will spent $26 on eTunes with a startup cost of $7.95 and $0.95 per song, how many songs did he download?

Back

Let x be the number of songs: 7.95 + 0.95x = 26. Solving gives x = 19.

Front

What is the algebraic equation for a table of values where y increases by 1 for every increase of 1 in x, starting from (0, -3)?

Back

The equation is y = x - 3.