Homework Flashcard 11/19/24

Front

What is the total cost formula for hosting a party at a restaurant with a per guest fee and a room reservation fee?

Back

Total Cost = (Cost per Guest * Number of Guests) + Room Reservation Fee

Front

How do you calculate the total cost for hosting a party for 6 guests at a restaurant that charges $15 per guest plus a $90 room fee?

Back

Total Cost = (15 * 6) + 90 = 180 dollars.

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line, typically in the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

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

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is point-slope form of a linear equation?

Back

Point-slope form is given by the equation y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Front

How do you write an equation in point-slope form for a line with a given slope and point?

Back

Use the point-slope formula: y - y1 = m(x - x1), substituting the slope and the coordinates of the point.

Front

What is slope-intercept form of a linear equation?

Back

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-intercept form of a line given two points?

Back

First, calculate the slope using the two points, then use one of the points to solve for the y-intercept (b) and write the equation in the form y = mx + b.

Front

What is the significance of parallel lines in terms of slope?

Back

Parallel lines have the same slope, meaning they will never intersect.

Front

What is the error made when writing an equation for a line parallel to another?

Back

The error is changing the slope to the opposite reciprocal instead of keeping it the same.