Cherie works in retail and her weekly salary includes...

Cherie works in retail and her weekly salary includes commission for the amount she sells. The equation $S=400+0.15 c$ models the relation between her weekly salary, $S$, in dollars and the amount of her sales, $c$, in dollars. (a) Find Cherie's salary for a week when her sales were 0 (b) Find Cherie's salary for a week when her sales were 3600 . (c) Interpret the slope and S-intercept of the equation. (d) Graph the equation.

Cherie works in retail and her weekly salary includes commission for the amount she sells. The equation $S=400+0.15 c$ models the relation between her weekly salary, $S$, in dollars and the amount of her sales, $c$, in dollars.
(a) Find Cherie's salary for a week when her sales were 0
(b) Find Cherie's salary for a week when her sales were 3600 .
(c) Interpret the slope and S-intercept of the equation.
(d) Graph the equation.

Key Concepts

Real-World Modeling

Real-world modeling with linear equations involves using mathematical equations to represent practical scenarios such as financial earnings or physical measurements. This approach translates tangible behaviors into abstract relationships, enabling predictions and interpretations of various real-life situations.

Linear Equations

A linear equation is a first-degree equation that represents a straight line when graphed on a coordinate plane. It models relationships where changes in one variable cause proportional changes in another, and is typically written in the form y = mx + b, where m is the slope and b is the y-intercept.

Slope

The slope in a linear equation quantifies the rate at which one variable changes relative to another. It represents the constant ratio of the change of the dependent variable to the change of the independent variable, indicating how steep the line is and the direction of the relationship.

Y-Intercept

The y-intercept of a linear equation is the value of the dependent variable when the independent variable is zero. It indicates where the line crosses the y-axis and often represents an initial value or fixed component in real-world models.

Graphing Linear Equations

Graphing a linear equation involves plotting a straight line on a coordinate plane using its slope and y-intercept. This visual representation aids in understanding the relationship between the variables, predicting values, and identifying key features like the rate of change and starting value.

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