Write an equation in point-slope form and slope-intercept form of the line passing through (-10,3) and (-2,-5).

Key Concepts

Point-Slope Form

Point-slope form of a linear equation is expressed as y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. This form is particularly useful for writing the equation of a line when you know a point on the line and its slope. It allows for easy identification of the slope and a specific point, making it straightforward to graph the line.

Slope-Intercept Form

Slope-intercept form is given by the equation y = mx + b, where m represents the slope of the line and b is the y-intercept. This form is beneficial for quickly identifying the slope and where the line crosses the y-axis. Converting from point-slope to slope-intercept form can help in graphing the line and understanding its behavior in relation to the coordinate axes.

Calculating Slope

The slope of a line measures its steepness and direction, calculated as the change in y divided by the change in x (m = (y2 - y1) / (x2 - x1)). For the points (-10, 3) and (-2, -5), the slope indicates how much y changes for a unit change in x. Understanding how to calculate the slope is essential for both point-slope and slope-intercept forms, as it directly influences the equations derived from these points.