Slope Intercept Form Word Problems Study Guide

These flashcards cover key concepts related to slope intercept form, equations derived from word problems, and calculations associated with linear relationships.

Slope Intercept Form

An equation of the form y = mx + b, where m is the slope and b is the y-intercept.

Initial Fee

The starting charge for a service, before any additional costs are added.

Equation of Total Cost for Recording

Given by Y = 35x + 50, where Y is the total cost, x is the number of hours, and each hour costs $35.

Value of a Car Over Time

The value of a new car decreases at a constant rate, resulting in a linear equation relating value to time.

Linear Equation for Height of a Tree

An equation that shows the relationship between the height of the tree and years after planting, represented as y = 2x + 8.

Slope (m) Calculation

The change in y over the change in x, calculated as (y2 - y1) / (x2 - x1).

Constants in Slope Intercept Form

In the equation y = mx + b, 'm' represents the slope, and 'b' represents the y-intercept.

Equations in Word Problems

Relations derived from real-life situations where variables represent quantities to be calculated.

Intercepts in Graphs

The points at which a line crosses the axes, specifically the y-intercept (0, b) in slope-intercept form.

Total Cost for Dance Instruction

Calculated using Y = 25x + 20, where Y is the total cost, and x is the number of hours of instruction.

Used Book Sale Total Cost

Expressed as Y = 7x + 3.10, relating the total cost to the number of books purchased.

Water Can Equation

Formed as Y = -2x + 68, showing the amount of water in the can decreases over time.

Coin Collection Growth Rate

Described by the equation Y = 9x + 20, linking the number of coins to days passed.

Constants from Problem Statements

Values determined through substitution into found equations to solve for 'b' or initial conditions.

Finding Variable Values

Using equations to determine unknown quantities by substituting known values into derived equations.