Writing Equations from Tables, Graphs, and 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 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

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 represented by the value of b in the equation y = mx + b.

Front

How do you write an equation from a table of values?

Back

To write an equation from a table, identify the pattern in the changes of x and y values, calculate the slope (m), and use a point to find the y-intercept (b).

Front

What is the purpose of graphing a linear equation?

Back

Graphing a linear equation helps visualize the relationship between variables and can be used to find solutions to the equation.

Front

How do you determine the equation of a line from a graph?

Back

To determine the equation of a line from a graph, find two points on the line, calculate the slope (m), and use one of the points to find the y-intercept (b).

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. Solutions to the system are the points where the equations intersect.

Front

How do you solve a system of equations graphically?

Back

To solve a system of equations graphically, graph each equation on the same coordinate plane and identify the point(s) where the lines intersect.

Front

What does it mean if a system of equations has no solution?

Back

If a system of equations has no solution, it means the lines are parallel and will never intersect.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

If a system of equations has infinitely many solutions, it means the equations represent the same line, and every point on the line is a solution.