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 of a line represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes (upward or downward).

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of $$b$$ in the equation $$y = mx + b$$ .

The y-intercept is 7, which is the value of $$b$$ in the equation.

The x-intercept is the point where the line crosses the x-axis. It can be found by setting $$y = 0$$ and solving for $$x$$ .

Set $$y = 0$$ : 0 = 4x - 1. Solving gives $$x = \frac{1}{4}$$ .

A negative slope means that as x increases, y decreases. The line goes downwards from left to right.

A positive slope means that as x increases, y also increases. The line goes upwards from left to right.

The standard form of a linear equation is $$Ax + By = C$$ , where A, B, and C are integers.

You can determine the correct graph by identifying the slope and y-intercept from the equation and comparing them to the graphs.