equation from 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 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 (b) 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 equation of a line from a table of values?

Back

To determine the equation, 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 formula to calculate the slope (m) between two points (x1, y1) and (x2, y2)?

Back

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

Front

If a table shows the values (1, 3) and (2, 5), what is the slope?

Back

The slope (m) is (5 - 3) / (2 - 1) = 2.

Front

What is the equation of a line with a slope of 2 and a y-intercept of 1?

Back

The equation is y = 2x + 1.

Front

How can you verify if a given equation matches a table of values?

Back

Substitute the x-values from the table into the equation and check if the resulting y-values match those in the table.

Front

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

Back

A negative slope indicates that as x increases, y decreases, meaning the line goes downwards from left to right.

Front

What is the significance of the equation y = mx + b?

Back

This is the slope-intercept form of a linear equation, where m is the slope and b is the y-intercept, providing a clear way to graph the line.