Graphing Linear Equations

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.

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).

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

To graph y = x - 4, start at the y-intercept (0, -4) and use the slope of 1 to rise 1 unit up and run 1 unit to the right to find another point.

The slope of the equation y = -¾x + 1 is -¾, indicating that for every 4 units you move to the right, you move down 3 units.

To graph y = ⅖x + 2, start at the y-intercept (0, 2) and use the slope of ⅖ to rise 2 units up and run 5 units to the right.

The slope of the equation y = 4x is 4, meaning for every 1 unit you move to the right, you move up 4 units.

To graph y = -2x + 4, start at the y-intercept (0, 4) and use the slope of -2 to fall 2 units down and run 1 unit to the right.

A line with a positive slope rises from left to right, indicating that as x increases, y also increases.

A line with a negative slope falls from left to right, indicating that as x increases, y decreases.