Linear Equations: Word Problems and Beyond

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 y-intercept represent in a linear equation?

Back

The y-intercept is the value of y when x is 0. It represents the starting point of the line on the y-axis.

Front

How do you interpret the slope in a linear equation?

Back

The slope (m) represents the rate of change of y with respect to x. It indicates how much y increases or decreases for each unit increase in x.

Front

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

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

How can you find the equation of a line given two points?

Back

To find the equation of a line given two points (x1, y1) and (x2, y2), first calculate the slope (m) using m = (y2 - y1) / (x2 - x1), then use one of the points to solve for b in the equation y = mx + b.

Front

What is the relationship between the slope and the direction of a line?

Back

If the slope is positive, the line rises from left to right. If the slope is negative, the line falls from left to right. A slope of zero indicates a horizontal line, while an undefined slope indicates a vertical line.

Front

How do you write an equation for a real-world situation?

Back

Identify the variables, determine the relationship between them, and express that relationship in the form of a linear equation.

Front

What does it mean for a linear equation to be in standard form?

Back

A linear equation is in standard form if it is written as Ax + By = C, where A, B, and C are integers, and A is non-negative.

Front

How do you convert from slope-intercept form to standard form?

Back

To convert from slope-intercept form (y = mx + b) to standard form (Ax + By = C), rearrange the equation to get all terms involving x and y on one side and the constant on the other.

Front

What is a word problem in the context of linear equations?

Back

A word problem is a mathematical problem that is presented in a narrative form, requiring the translation of the situation into a linear equation to find a solution.