Study Guide Unit 4

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, typically represented as 'm' in the slope-intercept form of a linear equation (y = mx + b). It is calculated as the change in y divided by the change in x (rise/run).

Front

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

Back

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

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 the y-intercept represent in a graph?

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

Write the equation in slope-intercept form for a plumber charging $25 for a service call plus $50 per hour of service.

Back

C = 25 + 50h.

Front

If Nicholas received $100 for his birthday and spends $20 per day, what is the equation representing his spending?

Back

y = -20x + 100.

Front

What is the y-intercept of the line represented by the equation y = -3x + 5?

Back

The y-intercept is 5, represented as the point (0, 5).

Front

How do you determine the y-intercept from a linear equation?

Back

To find the y-intercept, set x = 0 in the equation and solve for y.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as x increases, y decreases, meaning the line falls from left to right.

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as x increases, y also increases, meaning the line rises from left to right.