8.5I All Representations Review

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

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).

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

If a line has a slope of 5/2, what does this indicate about the line's steepness?

Back

A slope of 5/2 indicates that for every 2 units moved horizontally, the line rises 5 units vertically, making it relatively steep.

Front

Write the slope-intercept form of the equation for a line with a slope of 3 and a y-intercept of 4.

Back

y = 3x + 4.

Front

What is the total cost equation for a service that charges a flat fee plus a variable fee per unit?

Back

The total cost can be represented as y = mx + b, where m is the variable cost per unit and b is the flat fee.

Front

How do you determine the y-intercept from the equation y = 2x + 6?

Back

The y-intercept is 6, which means the line crosses the y-axis at the point (0, 6).

Front

What is the formula for calculating the total cost of renting equipment with a fixed fee and a per-hour charge?

Back

The formula is y = mx + b, where m is the hourly charge and b is the fixed rental fee.

Front

If a line is represented by the equation y = -2/3x + 5, what is the slope?

Back

The slope is -2/3, indicating the line falls as it moves from left to right.

Front

What does it mean if a slope is negative?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, resulting in a downward slant of the line.