7.4 Equations in Two Variables

Front

What is an equation in two variables?

Back

An equation that involves two different variables, typically represented as x and y, showing a relationship between them.

Front

What does the equation y = mx + b represent?

Back

It represents a linear equation where m is the slope and b is the y-intercept.

Front

In the equation y = 10x + 25, what does the number 10 represent?

Back

The slope of the line, indicating how much y changes for a unit change in x.

Front

How do you find the value of y when x = 3 in the equation y = 10x + 25?

Back

Substitute x with 3: y = 10(3) + 25 = 30 + 25 = 55.

Front

What is the dependent variable in the equation c = 0.15s?

Back

c (the commission) is the dependent variable because it depends on the value of s (the sale amount).

Front

What is the independent variable in the equation c = 0.15s?

Back

s (the sale amount) is the independent variable because it can be chosen freely.

Front

What does the constant in a linear equation represent?

Back

It represents the rate of change or the slope of the line.

Front

If the equation is d = 90t, what does 90 represent?

Back

The constant speed at which distance d changes with time t.

Front

How do you determine the slope from a graph?

Back

By calculating the rise over run between two points on the line.

Front

What is the formula to find the slope (m) between two points (x1, y1) and (x2, y2)?

Back

m = (y2 - y1) / (x2 - x1).