Linear Equations from Tables

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 is the y-intercept (b) in a linear equation?

Back

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

Front

How can you determine if a table of values represents a linear relationship?

Back

A table of values represents a linear relationship if the differences between consecutive y-values divided by the differences between consecutive x-values are constant.

Front

What is the formula for finding the slope between two points (x1, y1) and (x2, y2)?

Back

The formula for finding the slope (m) is m = (y2 - y1) / (x2 - x1).

Front

If a table shows the values (1, 2), (2, 4), (3, 6), what is the slope?

Back

The slope is 2, calculated as (4 - 2) / (2 - 1) = 2.

Front

What does it mean if the slope of a linear equation is negative?

Back

A negative slope indicates that as the x-values increase, the y-values decrease, meaning the line falls from left to right.

Front

How do you write the equation of a line given a slope and a point?

Back

Use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.

Front

What is the significance of a zero slope in a linear equation?

Back

A zero slope indicates a horizontal line, meaning there is no change in y as x changes.

Front

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

Back

Plot the points from the table on a coordinate plane and draw a straight line through them.