Writing Linear Equations from Word Problems

The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

The slope (m) represents the rate of change of y with respect to x, indicating how steep the line is.

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

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

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

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).

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

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

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.

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).