Writing Linear Equations from Word Problems

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope (m) represent in a linear equation?

Back

The slope (m) represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

Front

What does the y-intercept (b) represent in a linear equation?

Back

The y-intercept (b) is the value of y when x is 0. It is the point where the line crosses the y-axis.

Front

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

Back

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

Front

What is the point-slope form of a linear equation?

Back

The point-slope form of a linear equation is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

How do you write a linear equation from a word problem?

Back

Identify the variables, determine the relationship between them, and use the appropriate form of a linear equation based on the information given.

Front

What is the equation for a situation where a quantity decreases over time?

Back

The equation will have a negative slope, typically in the form y = mx + b, where m is negative.

Front

How do you represent a total cost in a linear equation?

Back

Use the form Ax + By = C, where A and B are the costs of different items, and C is the total cost.

Front

What is the significance of a non-refundable fee in a linear equation?

Back

A non-refundable fee is a fixed cost that is added to the total, represented as the y-intercept in the equation.