Writing Linear Equations from a Table

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 (m) represent in a linear equation?

Back

The slope (m) represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

Front

What does the y-intercept (b) represent in a linear equation?

Back

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

Front

How do you determine the slope from a table of values?

Back

To determine the slope from a table, calculate the change in y (rise) divided by the change in x (run) between two points: m = (y2 - y1) / (x2 - x1).

Front

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

Back

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

Front

How can you write a linear equation from a table of values?

Back

To write a linear equation from a table, identify the slope using two points from the table, then use one of the points to solve for the y-intercept.

Front

What is the significance of the initial deposit in a linear equation representing a bank account?

Back

The initial deposit represents the y-intercept (b) in the equation, indicating the starting amount in the account before any additional deposits.

Front

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

Back

To convert from standard form (Ax + By = C) to slope-intercept form (y = mx + b), solve for y to isolate it on one side of the equation.

Front

What is the relationship between the coefficients in a linear equation and the graph of the equation?

Back

The coefficients determine the slope and y-intercept of the line, affecting its steepness and position on the graph.

Front

How can you verify if a point lies on the line represented by a linear equation?

Back

To verify if a point (x, y) lies on the line, substitute the x-value into the equation and check if the resulting y-value matches the y-coordinate of the point.