In Exercises 11–38, use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Slope = 8, passing through (4, −1)

Key Concepts

Point-Slope Form

Point-slope form is a way to express the equation of a line when you know the slope and a point on the line. It is written as y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is the point. This form is particularly useful for quickly writing the equation of a line when given a slope and a specific point.

Slope-Intercept Form

Slope-intercept form is another way to express the equation of a line, defined as y = mx + b, where m is the slope and b is the y-intercept. This form is beneficial for easily identifying the slope and where the line crosses the y-axis. Converting from point-slope to slope-intercept form allows for a clearer understanding of the line's behavior.

Slope

The slope of a line measures its steepness and direction, calculated as the change in y over the change in x (rise over run). A positive slope indicates the line rises as it moves from left to right, while a negative slope indicates it falls. In this question, a slope of 8 means that for every unit increase in x, y increases by 8 units, which is crucial for forming the line's equation.