Writing 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 the y-value with respect to the x-value. It indicates how steep the line is.

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 slope (m) between two points (x1, y1) and (x2, y2) is calculated using the formula: $$m = \frac{y2 - y1}{x2 - x1}$$ .

Point-slope form is an equation of a line that passes through a given point (x1, y1) with a slope m, expressed as: $$y - y1 = m(x - x1)$$ .

The standard form of a linear equation is written as $$Ax + By = C$$ , where A, B, and C are integers, and A should be non-negative.

To convert from point-slope form $$y - y1 = m(x - x1)$$ to slope-intercept form $$y = mx + b$$ , solve for y.

The coefficients in a linear equation determine the slope and the y-intercept, which affect the line's steepness and position on the graph.

To graph a linear equation, identify the y-intercept, plot it on the graph, then use the slope to find another point and draw the line.

Parallel lines have the same slope but different y-intercepts, meaning they will never intersect.