Linear Word Problems

Front

What is a linear equation?

Back

A linear equation is an equation that represents 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

How do you identify the slope from a linear equation in standard form?

Back

To find the slope from a standard form equation (Ax + By = C), rearrange it into slope-intercept form (y = mx + b) and identify m.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes (positive or negative).

Front

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

Back

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

Front

What is the y-intercept in a linear equation?

Back

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

Front

How do you solve a linear equation?

Back

To solve a linear equation, isolate the variable on one side of the equation using inverse operations.

Front

What is the meaning of the x-intercept in a linear equation?

Back

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

Front

How can you determine the number of solutions to a system of linear equations?

Back

A system of linear equations can have one solution (intersecting lines), no solution (parallel lines), or infinitely many solutions (same line).

Front

What is the formula for calculating the slope between two points?

Back

The slope (m) between two points (x1, y1) and (x2, y2) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

How do you graph a linear equation?

Back

To graph a linear equation, find the x- and y-intercepts, plot them on a graph, and draw a straight line through these points.