Write 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 y with respect to x. It indicates how steep the line is and the direction it goes (positive slope goes up, negative slope goes down).

Front

What does the y-intercept (b) represent 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 do you find the slope from a table of values?

Back

To find the slope from a table, calculate the change in y divided by the change in x (rise/run) between two points.

Front

What is the equation of a line given two points (x1, y1) and (x2, y2)?

Back

The equation can be found using the slope formula m = (y2 - y1) / (x2 - x1) and then using point-slope form: y - y1 = m(x - x1).

Front

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

Back

The point-slope form is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Front

How can you convert a table of values into a linear equation?

Back

Identify the slope from the table, find the y-intercept, and then use the slope-intercept form y = mx + b.

Front

What is the slope of the line represented by the equation y = 3x - 9?

Back

The slope of the line is 3.

Front

What is the y-intercept of the line represented by the equation y = -2x + 10?

Back

The y-intercept of the line is 10.

Front

If a table shows that y increases by 6 when x increases by 2, what is the slope?

Back

The slope is 6/2 = 3.