Writing Linear Equations from Word Problems

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is 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 y with respect to x, indicating how steep the line is.

Front

How do you determine the y-intercept (b) in a linear equation?

Back

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

Front

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

Back

The slope-intercept form of a linear equation is y = mx + b.

Front

In the equation y = 25x + 40, what do the numbers 25 and 40 represent?

Back

In the equation y = 25x + 40, 25 represents the slope (rate per hour), and 40 represents the y-intercept (fixed service fee).

Front

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

Back

To write a linear equation from a word problem, identify the variables, determine the rate of change (slope), and find the fixed amount (y-intercept).

Front

What is the equation for a plant growing at a rate of 3cm per month starting from 5cm?

Back

The equation is y = 3x + 5, where y is the height of the plant and x is the number of months.

Front

What does the term 'application-based question' mean in the context of linear equations?

Back

An application-based question involves using linear equations to solve real-world problems, often presented in word problem format.

Front

How do you interpret the equation y = 12x in a real-world context?

Back

In the equation y = 12x, y represents the total miles walked, and x represents the number of weeks, indicating a consistent walking rate of 12 miles per week.

Front

What is the significance of the delivery fee in the equation y = 30 + 12.50x?

Back

The delivery fee of $30 is the fixed cost that must be added to the total cost of the meal, which varies based on the number of people (x).